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Using atmospheric noble gases and sulfur hexafluoride as indicators for transport and reaction processes… Jones, Katherine 2009

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USING ATMOSPHERIC NOBLE GASES AND SF6 AS INDICATORS FOR TRANSPORT AND REACTION PROCESSES IN HYDROCARBON CONTAMINATED SEDIMENTS  by Katherine Jones  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE  in  THE FACULTY OF GRADUATE STUDIES (Geological Science)  The University of British Columbia (Vancouver)  © Katherine Jones, 2009  Abstract  Naturally occurring contaminant attenuation processes are investigated in a petroleumhydrocarbon contaminated shallow aquifer, near Bemidji, MN. At this site, the biodegradation of hydrocarbons operates mostly under methanogenic conditions and generates CO2 and CH4. The main objectives of this study are to determine whether the full suite of noble gases, including He, Ne, Ar, Kr, and Xe, can be used to further delineate the fate of contaminants in the saturated and vadose zones and to identify mass transfer processes between these two compartments. Noble gases are sampled in the field and analyzed by way of an extraction line and mass spectrometry. In the vadose zone, gas consumption and production will induce pressure gradients, causing advective gas transport, which can be identified through concentration gradients of the inert gases. Noble gas data collected at the Bemidji site confirms the occurrence of advective gas transport, providing verification for previous field investigations and modeling that focused on Ar and N2 as gas tracers. In addition, the present study reveals that heavier noble gases provide the strongest signal for identifying reactioninduced gas advection in the vadose zone, as a result of their lower diffusion coefficients. The biogenic addition of gas to the saturated zone promotes gas exsolution and bubble formation, which can be marked in the source zone by the depletion of dissolved noble gas concentrations in relation to atmospheric values. Modeling results support the hypothesis that ebullition, the buoyancy-driven upward migration of gas bubbles, is taking place locally in the source zone. The flux of gas across the water table, as a result of ebullition, is estimated at 0.177Lm-2day-1. Ebullition is further investigated under laboratory closed system conditions. Results indicate that both atmospherically derived Ar and injections of SF6 can be used as tracers for ebullition. However, the partitioning of gas tracers into free-phase hydrocarbons limits the applicability of gas tracer injections. An oil-gas partitioning experiment is carried out to assess the feasibility of SF6 as a tracer in hydrocarbon contaminated settings. The results suggest that partitioning of SF6 into oil is extensive, with a dimensionless oil-gas partitioning coefficient of 0.73. ii  Table of Contents Abstract .......................................................................................................................... ii Table of Contents .......................................................................................................... iii List of Tables ................................................................................................................. vi List of Figures ................................................................................................................ ix Nomenclature ............................................................................................................... xv Acknowledgements .................................................................................................... xvii 1 Introduction ...............................................................................................................1 1.1 Petroleum Hydrocarbon Contamination .............................................................. 1 1.2 Nonreactive Gases ............................................................................................. 2 1.3 Vadose Zone Nonreactive Gas Transport ........................................................... 3 1.4 Gas Exsolution and Bubbles in Groundwater ......................................................4 1.5 Research Questions ........................................................................................... 5 2 Noble Gases as Transport and Reaction Tracers in the Vadose Zone of a Hydrocarbon Contaminated Shallow Subsurface............................................................ 7 2.1 Introduction .........................................................................................................7 2.2 Site Description.................................................................................................10 2.3 Vapor Phase Sample Collection and Analysis ..................................................14 2.3.1 Major Component Gas Sampling and Analysis ...........................................14 2.3.2 Vapor Phase Noble Gas Sampling ............................................................. 15 2.3.3 EAWAG Vapor Phase Noble Gas Analysis .................................................16 2.4 Results..............................................................................................................17 2.4.1 Major Gas Vadose Zone Sampling Results ................................................17 2.4.2 Noble Gas Vadose Zone Sampling Results ................................................19 2.4.3 Method Comparison ...................................................................................21 2.5 Discussion ........................................................................................................23 2.5.1 Total Pressure Variations in the Reaction Zones ........................................23 2.5.2 Background Conditions ...............................................................................24 2.5.3 Elemental Ratio Analysis ............................................................................25 2.5.4 Temperature Effects ...................................................................................26 2.5.5 Noble Gas Profiles ......................................................................................27 2.6 MIN3P-DGM Noble Gas Migration Model .........................................................33 2.6.1 The Dusty Gas Model .................................................................................33 2.6.2 Model Parameters ......................................................................................35 2.6.3 601 Model Results ......................................................................................39 2.6.4 MIN3P- DGM Discussion for Profile 601 .....................................................40 2.6.5 532 Model Results ......................................................................................45 2.6.6 MIN3P-DGM Discussion for Profile 532 ......................................................46 2.7 Conclusions ......................................................................................................48 3 Dissolved Noble Gas Concentrations as Tools to Evaluate Degassing and Ebullition in Hydrocarbon Contaminated Settings ........................................................................50 3.1 Introduction .......................................................................................................50 3.2 Dissolved Gas Sample Collection and Analysis ................................................55 iii  3.2.1 Dissolved Noble Gas Sampling ..................................................................55 3.2.2 EAWAG Dissolved Noble Gas Analysis ......................................................56 3.3 Results..............................................................................................................57 3.4 Discussion ........................................................................................................65 3.4.1 Kinetic Fractionation ...................................................................................65 3.4.2 He Data ......................................................................................................70 3.4.3 Solubility Controlled Fractionation............................................................... 72 3.4.4 Partitioning of Gases into Oil ......................................................................73 3.4.5 Excess Air ..................................................................................................74 3.4.6 Diffusion of Noble Gas in Pore Water and Dissolved Noble Gas Replenishment – Empirical Findings......................................................................76 3.4.7 Groundwater Mixing as a Result of Advection- Empirical Findings..............77 3.4.8 Relating Dissolved Concentrations to Methanogens ...................................79 3.5 Groundwater Flow Modeling .............................................................................82 3.6 Reactive Transport Ebullition-Inclusive Modeling ..............................................85 3.6.2 Initial Conditions .........................................................................................89 3.6.3 Steady State Modeling of Degassing Ratios ...............................................91 3.6.4 Steady State Modeling for Systems without Ebullition.................................93 3.6.5 Transient Modeling for Systems without Ebullition ......................................95 3.6.6 Steady State Ebullition Model .....................................................................96 3.6.7 Model Limitations ...................................................................................... 101 3.7 Conclusion ...................................................................................................... 101 4 Laboratory Assessment of the Effectiveness of Nonreactive Gases as Tracers for Ebullition..................................................................................................................... 103 4.1 Introduction ..................................................................................................... 103 4.2 Part 1: Partitioning Experiment ....................................................................... 105 4.2.1 Sample Preparation .................................................................................. 105 4.2.2 Gas Analysis............................................................................................. 107 4.2.3 Results of Partitioning Experiment ............................................................ 107 4.2.4 Discussion of Partition Experiment ........................................................... 108 4.3 Part 2: Column Experiment ............................................................................. 111 4.3.1 Column Construction ................................................................................ 111 4.3.2 Composition of Column Fill ....................................................................... 113 4.3.3 Tracer Test Method .................................................................................. 114 4.3.4 OmniStar Gas Analyzer Method ............................................................... 114 4.3.5 Results of Column Experiment ................................................................. 116 4.3.6 Biogenic Gas Production in the Column.................................................... 121 4.3.7 PhreeqC Gas Simulation of Column Experiment ...................................... 122 4.3.8 Discussion of Column Experiment ............................................................ 132 4.4 Conclusion ...................................................................................................... 139 5 Relating Saturated and Unsaturated Gas Transport Mechanisms in a Hydrocarbon Contaminated Setting ................................................................................................. 141 5.1 Introduction ..................................................................................................... 141 5.2 Applying Laboratory Findings to the Field Site ................................................ 141 5.2.1 Physical Column Measurements Applied to Bemidji Field Data ................ 141 5.2.2 Potential of SF6 as a Gas Tracer at Bemidji Site ....................................... 142 5.2.3 Argon Comparisons .................................................................................. 142 iv  5.3 Coupling of the Ebullition Flux to Vadose Zone Gas Transport at the Bemidji Site 143 5.3.1 Coupling of the Biogeochemical Reaction Zones at the Site ..................... 143 5.3.2 Empirical Evidence Supporting Ebullition with the Dissolved and Vapor Phase Noble Gases ............................................................................................ 144 5.3.3 Relating the MIN3P-DGM Modeling Results to the Ebullition Model Results 147 5.3.4 MIN3P-DGM Model - Noble Gas Component and an Inclusive Ebullition Flux 149 5.3.5 MIN3P-DGM Discussion for Profile 601, with Ebullition Considerations .... 152 5.4 Conclusion ...................................................................................................... 156 6 Summary and Conclusions ................................................................................... 157 Works Cited................................................................................................................ 163 Appendix A ................................................................................................................. 169 Appendix B ................................................................................................................. 174 Appendix C ................................................................................................................. 177 Appendix D ................................................................................................................. 178 Appendix E ................................................................................................................. 179 Appendix F ................................................................................................................. 185 Appendix G. ............................................................................................................... 187 Appendix H ................................................................................................................. 191 Appendix I .................................................................................................................. 194  v  List of Tables Table 2.1. Isotopic composition of atmospheric noble gases (from Andrews, 1979) .....20 Table 2.2. Henry’s constant values added to the MIN3P-DGM database .....................36 Table 2.3. Gas viscosities and Lennard-Jones potentals specified in the input file implemented in MIN3P-DGM transport modeling...................................................37 Table 2.4. Literature parameters for physical aquifer attributes at the Bemidji site........38 Table 2.5. Profile port locations with depth ..................................................................39 Table 2.6. Assigned aquifer property variables at profile 601 implemented in the MIN3PDGM modeling ......................................................................................................40 Table 2.7. Assigned aquifer property variables at profile 532 implemented in MIN3PDGM modeling ......................................................................................................45 Table 3.1. Henry’s coefficients for noble gases at 10°C at 1 atm and 0 ‰ salinity, and manipulation thereof. All values are calculated from data collected in Benson and Krause (1976) .......................................................................................................57 Table 3.2. Vadose zone mole fractions converted to dissolved concentrations for paired vadose zone – saturated zone wells at the Bemidji site .........................................58 Table 3.3. Dissolved noble gas concentrations normalized to the atmospheric dissolved noble gas concentrations at monitoring wells positioned along the axis of the plume of the north pool at the Bemidji site .......................................................................59 Table 3.4. Dissolved noble gas concentrations normalized to the background dissolved concentrations at monitoring well positioned along the axis of the plume of the north pool at the Bemidji site .................................................................................61 Table 3.5. Dissolved noble gas concentrations normalized to the paired vadose zone dissolved noble gas concentrations at monitoring wells positioned along the axis of the plume of the north pool at the Bemidji site .......................................................63 Table 3.6. Dissolved noble gas isotopic ratios measured at monitoring wells along the plume axis of the north pool at the Bemidji site ......................................................66 Table 3.7. Rayleigh fractionation line calculations using 22Ne associated fractionation for the defined isotope ratios .................................................................................69 Table 3.8. Calculated diffusion coefficients of dissolved gases in solution at 10°C ......76 Table 3.9. Monitoring well construction data coupled with estimates of methanogen counts as approximated by the most probably number technique .........................78  vi  Table 3.10. Aquifer properties and parameters and the associated literature values implemented in the saturated zone Modflow modeling of the Bemidji aquifer ........83 Table 3.11. Modflow monitoring well locations and screen depths and estimated particle path lengths, as calculated by Modflow and by velocity ratios ...................85 Table 3.12. Modeling parameters associated with reactive transport ebullition modeling at monitoring well 315 ........................................................................................... 87 Table 3.13. Modeled dissolved noble gas concentrations normalized to actual 315 concentrations at steady state for degassing ratios not including ebullition events, and the associated biogenic gas additions and bubble volume increases, for specified gas saturation levels ...............................................................................93 Table 3.14. Modeled dissolved noble gas concentrations normalized to actual 315 concentrations at steady state and the associated biogenic gas additions and bubble volume increases for specified gas saturation levels ..................................97 Table 3.15. Overall findings pertaining to the steady state reactive transport ebullition modeling conducted at the Bemidji site at monitoring well 315 ............................ 101 Table 4.1. Summary table of partitioning experiment SF6 sample details................... 106 Table 4.2. Calibration standard preparations volumes implemented in the analysis of the SF6 oil-gas partitioning experiment associated with the OmniStar Gas Analyzer readings .............................................................................................................. 107 Table 4.3. SF6 mole fractions in the headspace of oil-gas partitioning experiment samples, upon equilibration with the oil phase, as measured by OmniStar Gas Analyzer .............................................................................................................. 108 Table 4.4. Total moles of SF6 in the gas and oil phase, at equilibrium, for samples analyzed in the oil-gas partitioning experiment .................................................... 109 Table 4.5. Dimensionless partitioning coefficients of SF6 for oil-gas partitioning, airwater partitioning, and oil-water partitioning......................................................... 111 Table 4.6. Column construction details for the column ebullition experiment ............. 113 Table 4.7. Omnistar Gas Analyzer – Column method setup details ........................... 115 Table 4.8. Initial column physical measurements for the ebullition column experiment ............................................................................................................................ 116 Table 4.9. Initial headspace conditions of the column experiment ............................. 118 Table 4.10. Input parameters for the PhreeqC modeling of the ebullition column experiment .......................................................................................................... 125 Table 4.11. Supplements to the PhreeqC data base implemented into OMZ input file ............................................................................................................................ 126  vii  Table 4.12. Approximate amount of methane produced and consumed during the course of the column experiment. ........................................................................ 134 Table 5.1. Ar/Xe ratios in both the dissolved and vapor phases at the Bemidji site .... 145 Table 5.2. A comparison of the possible ebullition flux as calculated by the MIN3PDGM model and the ebullition model ................................................................... 148 Table 5.3. Summary table of the values used to calculate the theoretical nonreactive gas composition of the source term implemented during MIN3P-DGM modeling 150 Table 5.4. Assigned aquifer property variables at profile 601 implemented in MIN3PDGM modeling, with an inclusive ebullition flux ................................................... 151 Table A.1. Major component gas dataset for vadose zone gas analyzed with the CP4900 Varian gas chromatograph during 2008 sampling event, Bemidji, Minnesota ............................................................................................................................ 169 Table B.1. Noble gas dataset for vadose zone gas analyzed through noble gas extraction lines and mass spectrometry at EAWAG during 2008 sampling event, Bemidji, Minnesota .............................................................................................. 174 Table B.2. Noble gas isotope ratio dataset for vadose zone gas analyzed through noble gas extraction lines and mass spectrometry at EAWAG during 2008 sampling event, Bemidji, Minnesota ................................................................................... 176 Table C.1. Geological bore hole logs recorded at monitoring well 423, situated south east of well 601 ................................................................................................... 177 Table D.1. Noble gas dataset for dissolved gas analyzed through noble gas extraction lines and mass spectrometry at EAWAG during 2008 sampling event, Bemidji, Minnesota............................................................................................................ 178 Table D.2. Noble gas isotope ratio dataset for dissolved gas analyzed through noble gas extraction lines and mass ............................................................................. 178 Table F.1. Detection potentials for SF6 as a tracer for ebullition, in a hydrocarbon setting, with a maximum gas saturation rate of 10% ............................................ 185 Table G.1. Column physical parameters and headspace mole fractions for the column experiment .......................................................................................................... 187 Table H.1. PhreeqC results for column experiment .................................................... 192 Table I.1. Methane headspace volume and mole calculations for column experiment 197 Table I.2. Oxygen headspace volume and mole calculations for column experiment.. 200 Table I.3. Argon headspace volume and mole calculations for column experiment .... 201 Table I.4. SF6 headspace volume and mole calculations for column experiment ........ 204  viii  List of Figures Figure 2.1. Bemidji research site location. The figure is based on data presented in USGS (2009). ........................................................................................................11 Figure 2.2. Plan view of the Bemidji field site and the locations of the hydrocarbon plumes present at the site. Figure was based on data collected from USGS (2009). .............................................................................................................................. 12 Figure 2.3. A cross section intersecting the extent of the Bemidji site, positioned through the axis of the north plume, detailing the position of the LNAP, and the relevant site geology. Site geology is based on data presented in Smith and Hult (1993).........13 Figure 2.4. A cross section along the axis of the north plume, detailing the position of the vapor wells that are sampled during noble gas analysis, the position of the LNAP, and the relevant site geology......................................................................14 Figure 2.5. A cross section along the axis of the north plume, detailing the position of the vapor wells that are sampled during noble gas analysis, the position of the LNAP, the relevant site geology and the location of the methanotrophic zone. The methanotrophic zone is approximated by contouring O2 and CO2 vadose zone measurements that were obtained with a Varian CP-4900 GC during the 2008 sampling session. ..................................................................................................18 Figure 2.6. Vadose zone noble gas volume fractions normalized to atmospheric values sampled from vapor wells located along the axis of the north plume. Atmospheric values are delineated by the straight line intersecting the graph. ........................... 21 Figure 2.7. A side by side comparison of vadose zone argon gas volume fractions sampled from vapor wells located along the axis of the north plume, measured with a Varian 4900 GC or by the EAWAG methods. .....................................................22 Figure 2.8. A cross section along the axis of the north plume detailing the simulated gas pressures as % deviation from atmospheric levels. Shaded areas indicate zone of elevated (dark) and lowered (light) pressure. The figure is modified from (Molins et al., 2009). ..............................................................................................................24 Figure 2.9. Vadose zone noble gas volume fraction ratios normalized to atmospheric values sampled from vapor wells located along the axis of the north plume. Atmospheric values are delineated by the straight line intersecting the graph. ......25 Figure 2.10. Conceptual model applied to vadose zone noble gas transport at vapor well 601. ................................................................................................................28 Figure 2.11. Conceptual model applied to vadose zone noble gas transport at vapor well 532. ................................................................................................................29 Figure 2.12. A profile plotted with depth of vadose zone noble gas volume fractions normalized to atmospheric values at vapor well 601. Atmospheric values are delineated by the straight line intersecting the graph. ............................................30 ix  Figure 2.13. A profile plotted with depth of vadose zone noble gas volume fractions normalized to atmospheric values at vapor well 532. Atmospheric values are delineated by the straight line intersecting the graph. ............................................31 Figure 2.14. A profile plotted with depth of vadose zone noble gas volume fraction ratios normalized to atmospheric values at vapor well 601. Atmospheric values are delineated by the straight line intersecting the graph. ............................................32 Figure 2.15. A profile plotted with depth of vadose zone noble gas volume fraction ratios normalized to atmospheric values at vapor well 532. Atmospheric values are delineated by the straight line intersecting the graph. ............................................33 Figure 2.16. Vertical profiles of modeling results and field measurements for major component gas mole fractions at vapor well 601. Figure A illustrates modeling results of a homogenous subsurface. Figure B illustrates modeling results for a layered heterogeneous subsurface with a lower permeability layer in the lower portion of the domain. ............................................................................................ 41 Figure 2.17. Vertical profiles of modeling results and field measurements for noble gas mole fractions at vapor well 601. Figure A illustrates modeling results of a homogenous subsurface. Figure B illustrates modeling results for a layered heterogeneous subsurface, with a lower permeability layer in the lower portion of the domain. ...........................................................................................................42 Figure 2.18. Vertical profiles of the advective, diffusive, non-equimolar and DGM flux at vapor well 601 for a layered heerogeneous system, with a lower permeability strata in the lower portion of the domain. Plots illustrate system fluxes for O2, CH4, CO2, Ne, and Xe, respectively. .......................................................................................44 Figure 2.19. Vertical profile of modeling results and field measurements for major component gas mole fractions at vapor well 532, in a homogenous subsurface. ...46 Figure 2.20. Vertical profile of modeling results and field measurements for noble gas mole fractions at vapor well 532 in a homogenous subsurface. ............................. 47 Figure 2.21. Vertical profiles of the advective, diffusive, non-equimolar and DGM flux at vapor well 532. Plots illustrate system fluxes for O2, CH4, CO2, Ne, and Xe, respectively. ..........................................................................................................48 Figure 3.1. Core sample recovered from the source zone of the Bemidji site. The figure is adapted from Amos et al. (2005). The core samples on the left and centre left were recovered from the vicinity of vapor well 9014, at a depth intervals 421.3 m to 423.5 m. The core samples on the right were recovered in 1997 from the vicinity of monitoring well 421. The diameter of each core is 47 mm. ...................................53 Figure 3.2. Conceptual model applied to dissolved noble gas transport in the saturated zone of the highly methanogenic sediment at the Bemidji site. .............................. 54 Figure 3.3. A cross section along the axis of the north plume detailing the position of the vapor wells and monitoring well that are sampled during noble gas analysis, the position of the LNAPL, and the relevant site geology. ............................................55 x  Figure 3.4. In field photograph of a noble gas water sample and sampling apparatus, collected for noble gas analysis at EAWAG. .......................................................... 56 Figure 3.5. Dissolved noble gas concentrations in units of cm3(STP)/g normalized to theoretical dissolved noble gas concentrations associated with atmospheric gas sampled from monitoring wells located along the axis of the north plume. Atmospheric values are delineated by the straight line intersecting the graph. ......60 Figure 3.6. Dissolved noble gas concentrations in units of cm3(STP)/g normalized to background concentrations (MW 310), sampled from monitoring wells located along the axis of the north plume. Background values are delineated by the straight line intersecting the graph. ........................................................................................... 62 Figure 3.7. Dissolved noble gas concentrations in units of cm3(STP)/g normalized to theoretical dissolved noble gas concentrations associated with overlying vadose zone gas volume fractions sampled from monitoring wells located along the axis of the north plume. Vadose zone values are delineated by the straight line intersecting the graph. ........................................................................................... 64 Figure 3.8. Dissolved noble gas 22Ne/20Ne ratios and 40Ar/36Ar ratios sampled from monitoring wells located along the axis of the north plume. ...................................66 Figure 3.9. Dissolved 20Ne/22Ne ratios plotted against dissolved 36Ar/40Ar sampled from monitoring wells located along the axis of the north plume and the site specific Rayleigh fractionation line calculated at fractionation values of 1 and 0.5 as determined by theoretical 22Ne values. ..................................................................70 Figure 3.10. Dissolved 3He/4He ratios sampled from monitoring wells located along the axis of the north plume. .........................................................................................71 Figure 3.11. Dissolved 20Ne/22Ne ratios plotted against dissolved 3He/4He,sampled from monitoring wells located along the axis of the north plume and the site specific Rayleigh fractionation line, calculated at fractionation values of 1 and 0.5 as determined by theoretical 22Ne values. ..................................................................72 Figure 3.12. Dissolved noble gas ratios normalized to theoretical dissolved noble gas concentrations associated with dissolved overlying vadose zone gas volume fractions sampled from monitoring wells located along the axis of the north plume. Vadose zone values are delineated by the straight line intersecting the graph. .....73 Figure 3.13. Dissolved noble gas concentrations at 533C in units of cm3(STP)/g normalized to background concentrations as a function of each respective diffusion coefficients at 10°C, as estimated from Jähne et al. (1987). ..................................77 Figure 3.14. Dissolved noble gas concentrations measured in units of cm3(STP)/g normalized to background concentrations (MW 310) sampled from monitoring wells screened at similar depths located along the axis of the north plume. Background values are delineated by the straight line intersecting the graph. ........................... 79 Figure 3.15. The log MPN counts of methanogens per g of saturated sediment plotted against along the axis of the north plume, modified from Bekins et al. (2005)........80 xi  Figure 3.16. Ar/Kr ratios of source zone wells normalized to theoretical dissolved noble gas concentrations associated with overlying vadose zone gas volume fractions as a function of MPN methanogen count, as reported by Bekins et al. (2005). ...........81 Figure 3.17. Methanogen MPN count per g of sample with depth, at three locations along the axis of the plume modified from information provided by Bekins et al. (2001). Methanogenic zones within the saturated zone are estimated and plotted along the cross section along the axis of the north plume......................................82 Figure 3.18. Modflow domain as it applies to the Bemidji cross-section. Silt layers in the model are represented as lower conductivity layers. The lower till boundary is represented as an impermeable boundary. Methanogenic zones signify zones of high gas production. Equipotential lines and particle path lines are simulated under steady states conditions. The monitoring well and vapor well locations are illustrated along the axis of the north plume........................................................... 84 Figure 3.19. Conceptual model detailing the Lagrangian style reactive transport modeling of dissolved noble gases in the saturated zone of the highly methanogenic sediment at monitoring well 315. ....................................................88 Figure 3.20. Dissolved noble gas concentrations, at well 315, as simulated by the degassing only model, normalized to actual dissolved concentrations of He, Ne, Ar, Kr, and Xe, for gas saturation values of 5% and 20% for steady state modeling without ebullition. ...................................................................................................94 Figure 3.21. Dissolved noble gas concentrations at well 315 as simulated by the transient model, normalized to the actual dissolved concentrations of Ar, Kr, and Xe, for an initial gas saturation values of 0%. The gas saturation values are allowed to increase with time and are represented on the lower x-axis. Ebullition is not considered in the system. The boundary conditions imposed on the transient model are those of current day vadose zone dissolved gas concentrations. ..........96 Figure 3.22. Noble gas concentrations at well 315, as simulated by the ebullition model, normalized to actual dissolved concentrations of He, Ne, Ar, Kr, and Xe, for gas saturation values of 5% (A), 10% (B), and 20% (C) at steady state conditions Ebullition is removed from the model for the 5 % gas saturation model during the final 3 time steps, and degassing is allowed to ensue. ..........................................98 Figure 3.23. Noble gases concentrations, at well 315, as simulation by the ebullition model at a gas saturation of 10%, normalized to vadose zone concentrations, plotted against depth for monitoring well 310. The biogenic gas production rate is 1.28 mmols per cell, or a rate of 5.78 x 10-10mols Lpore water-1s-1. ........................... 100 Figure 4.1. For samples in the oil-gas partitioning experiment, the total moles of SF6 contained within the oil, plotted against the total moles of SF6 in the headspace, at equilibrium. .......................................................................................................... 110 Figure 4.2. Ebullition column details, with the column constructed out of 2 cm Plexiglas. The base of the column contains a ball valve used for tracer injections. A second ball valve is located midway up the column. A pressure relief port is located at the top of the column. The column is fitted with an Ashcroft low pressure gauge and an xii  additional port, which is attached to an OmniStar Gas Analyzer. The column consists of a sediment phase, water phase and a gas phase. The sediment phase consists of an organic matter zone, a gravel zone, and a 30 mesh Ottawa sand zone. ................................................................................................................... 112 Figure 4.3. Water level change and accumulative volume of gas released from the columns as a result of biogenic gas production. .................................................. 117 Figure 4.4. Column headspace reactive gas % composition determined with an OmniStar Gas Analyzer. ...................................................................................... 119 Figure 4.5. Column headspace nonreactive gas % composition determined with an OmniStar Gas Analyzer. ...................................................................................... 119 Figure 4.6. Conceptual model detailing gas transport in the PhreeqC simulation of the OMZ of the column. ............................................................................................. 124 Figure 4.7. Moles of CH4 and CO2 in the entrapped gas phase of the OMZ, which is subject to ebullition and thus occupies a relatively constant volume, in a close column environment plotted as a function of the volume of biogenic gas produced. ............................................................................................................................ 127 Figure 4.8. Moles of nonreactive gas in entrapped gas phase in the OMZ, which is subject to ebullition and thus occupies a relatively constant volume, in a closed system environment, plotted as a function of the volume of biogenic gas produced. ............................................................................................................................ 128 Figure 4.9. Molality of noble gases dissolved in the pore water of the OMZ, where the entrapped gas phase is subject to ebullition, and thus occupies a relatively constant volume, in a closed system environment, plotted as a function of the volume of biogenic gas produced. ....................................................................................... 129 Figure 4.10. Molality of noble gases dissolved in the pore water of the OMZ, where the entrapped gas phase is not subject to ebullition, in a closed system environment, plotted as a function of the volume of biogenic gas produced. ............................. 130 Figure 4.11. Ar/Xe dissolved noble gas ratio in the OMZ of a closed system environment, plotted as a function of the volume of biogenic gas produced, for systems including and excluding ebullition. ......................................................... 131 Figure 4.12. Moles of methane entering the column headspace during the ebullition column experiment as a function of the volume of biogenic gas produced. Moles of methane were measured with the OmniStar Gas Analyzer. ................................. 133 Figure 4.13. Moles of methane entering the head space of the column during the column experiment as a function of time. Moles of methane were measured with the OmniStar Gas Analyzer. ................................................................................ 133 Figure 4.14. Volume of O2 in the headspace of the column during the column ebullition experiment as a function of time. The theoretical moles of O2, assuming no O2 is consumed are illustrated, as is the predicted volume of moles consumed. .......... 135 xiii  Figure 4.15. Volume of Ar in the headspace during the column ebullition experiment as a function of time. Mole fractions of O2 were measured with the OmniStar Gas Analyzer. The theoretical decline in headspace argon assuming 0 argon storage in the column is illustrated. ...................................................................................... 137 Figure 4.16. Moles of SF6 in the column headspace during the column ebullition experiment. Moles of SF6 are measured with the OmniStar Gas Analyzer. ......... 138 Figure 5.1. A cross section intersecting the extent of the Bemidji site positioned along the axis of the north plume detailing the position of the vapor wells and monitoring wells that are sampled during noble gas analysis, the position of the LNAP, the location of the methanotrophic and methanogenic zones, and the relevant site geology. .............................................................................................................. 144 Figure 5.2. Ar/Xe ratios of noble gas mole fractions in the vadose zone plotted against dissolved concentrations in the saturated zone in monitoring and vapor well couplings located along the axis of the north plume. Monitoring wells are indicated on the figure. ....................................................................................................... 146 Figure 5.3. Conceptual model applied to vadose zone gas transport with an inclusive ebullition component incorporated into the model at vapor well 601. ................... 149 Figure 5.4. Vertical profile of modeling results and field measurements for major component gas mole fractions, at monitoring well 601 in a layered heterogeneous subsurface. An ebullition flux is included in the model calibration. ...................... 153 Figure 5.5. Vertical profile of modeling results and field measurements for noble gas mole fractions, at monitoring well 601 in a layered heterogeneous subsurface. An ebullition flux is included in the model calibration................................................. 154 Figure 5.6. Veritical profiles of the advective, diffusive, non-equimolar and DGM flux at vapor well 601 in a layered heterogeneous subsurface. An ebullition flux is included in the model calibration. Plots illustrate system fluxes for O2, CH4, CO2, Ne, and Xe, respectively. ..................................................................................... 155 Figure A.1. The vapor well locations of wells sampled for major component gas analysis. All wells are located along the axis of the north plume. ........................ 173  xiv  Nomenclature Variable Explanation  Units  B  # of cells  #  Ci  concentration of species i  mol L-1  C  concentration  mol L-1  CG  concentration in gas phase  mol L-1  CO  concentration dissolved in oil  mol L-1  Cs  substrate concentration where v = 1 2v max  mol L-1  CW  concentration in water  mol L-1  Di  mass dependent diffusion coefficient  m2 s-1  Dij  effective molecular diffusion coefficient i of in j  m2 s-1  f  fractionation parameter  unitless  h  altitude  m  hs  scale height  m  k  rate constant  mol L-1 time-1  kH  Henry’s constant  atm [mol L-1]-1  k Hx  Henry’s constant  unitless  k Hpx  Henry’s constant  atm [mol mol-1]-1  k HSTP  Henry’s constant  atm cm-3(STP)L-1  K G −W  gas-water partitioning coefficient  unitless  KO−G  oil-gas partitioning coefficient  unitless  KO−W  oil-water partitioning coefficient  unitless  Mb  mass of medium  mass  Mi  mass of species i  mass  M i*  reduced mass  mass  ni  number of moles of component i  mol  nG  number of moles in the gas phase  mol  nT  total number of moles  mol  nO  number of moles dissolved in oil  mol  N iD  molar diffusive flux  mol m-2 s-1 xv  Variable  Explanation  Units  N iT  mol m-2 s-1  P  total molar gas flux i of relative to a fixed coordinate system total pressure  pi  partial pressure of component i  atm / kPa  Pi  final calculated pressure  atm / kPa  Po  initial daily pressure  atm / kPa  p sl  pressure at sea level  atm / kPa  PT ,o  standard pressure  atm / kPa  R  universal gas constant  L atm K−1 mol−1  S  substrate  mol L-1  T  temperature  K  To  standard temperature  K  v  rate of substrate uptake  mol time-1  V  volume  L / mL/ cm3/ m3  Vi  final calculated volume  L / mL / m3  Vo  initial daily headspace volume  L / mL / m3  v max  maximum rate of substrate uptake  mol time-1  VR  released volume  L / mL / m3  Xi  mole fraction of component i  unitless  ρw  density of water ≈ 1  g cm-3  atm / kPa  xvi  Acknowledgements  First and foremost, I would like to thank Dr. Uli Mayer for giving me the chance to work with various modeling codes and gas analysis instrumentation, and for allowing me the opportunity to travel to Antamina Peru to conduct research in a zinc and copper mine. I am very grateful to Dr. Mayer for introducing me to the wonderful people at the USGS but most of all I would like to extend my deepest gratitude to Dr. Mayer for sending me to EAWAG in Switzerland, where I was afforded the opportunity to work in one of the world’s most advanced noble gas laboratories.  I would also like to take this opportunity to thank Dr. RoKi Kipfer, a professor at ETH and EAWAG, in Zurich, Switzerland. Although my time at ETH was short, the kindness that was extended to me during my stay went beyond any expectations. Not only was I invited into the laboratory, but the instruction and laboratory freedom I received while at ETH was exceptional. Furthermore, I would like to thank all of the 2007/2008 USGS Bemidji field site workers, in particular, Jared Trost, Ben Cowie, Dr. Barbara Bekins, and Geoff Delin.  I am much obliged to Dr. Roger Beckie, and Dr. Leslie Smith, as I learned a great deal from both of them during the pursuit of this Master of Science degree. Furthermore, I would like to show my appreciation to Dr. Roger Beckie and Dr. Philippe Tortell for providing guidance during my committee meetings. I would also like to recognize Joern Unger, whose technical skills I would regularly recruit during the construction of my many laboratory apparatuses, and Laxmi Chikatamarla, who was always willing to lend a spare part, and great advice, for various scientific endeavors. Finally I would like to thank Dr. Sergi Molins, who gave me his modeling code, and his ear for various scholastic obstacles I encountered throughout this experience.  xvii  1  1.1  Introduction  Petroleum Hydrocarbon Contamination  Subsurface petroleum hydrocarbon contamination is a widespread environmental problem that is often remediated through biodegradation techniques. Oil is the most common subsurface contaminant and accounts for 58% of all reported contaminant spills in Canada (Environment Canada, 2006). Petroleum hydrocarbon spills are multiphase and can exist as free or residual phase contaminants, as well as in dissolved or vapor form. Remediation techniques can include both active and passive methods. The active cleanup of hydrocarbon contamination can be difficult, as a result of residual contamination, and is often costly. Natural attenuation refers to the passive breakdown of hydrocarbons, catalyzed by the native soil microbes, the efficiency of which will decline with a lowering in the redox state of the subsurface. The size and saturation level of the hydrocarbons (exemplified by CH2O) will influence the effectiveness of hydrocarbon degradation, as will as site-specific physical properties and the biology of the aquifer. As a result, source and plume longevities are highly variable.  The rate, and ultimately, the success of biodegradation can be quantified by a carbon mass balance assessment. The degradation of organic matter is often described by the Michaelis-Menten decay equation: v  v =  max + S SB  Cs   [1]  where, S is the substrate [mol L-1], B is the number of cells, v is the rate of substrate uptake [mol time-1], v max is the maximum rate of substrate uptake [mol time-1], and Cs is the substrate concentration when v = 1 2v max [mol L-1]. So long as the microbial populations in the sediments remain constant (Chapelle, 1996), the decay of organic matter can be approximated by first order kinetics. The rate constant k [mol L-1 time-1] 1  is expressed as a change in concentration C [mol L-1] with time ( t ). k=  ∂C ∂t  [2]  In order for hydrocarbon degradation to proceed, the microbes require a supply of nutrients, as well as the presence of compatible electron acceptors. Once the most efficient electron acceptors are preferentially depleted, and the system is found to be in the lowest redox state, the mechanism behind the decay of organic matter becomes fermentation and methanogenesis, where the hydrocarbons themselves can act as the terminal electron acceptors. 2CH2O (aq) →CO2(aq) + CH4 (aq) CH4 can also be subject to bacterially mediated degradation during CH4 oxidation whereby methanotrophs will use O2 as the electron acceptor and CH4 as the substrate. 2O2(g) + CH4(g)→CO2(g) + 2H2O The type of reactions taking place within the subsurface, and the rate at which these reactions occur, are devices used to help quantify the fate of contaminants in sediments. The consumption and the formation of gases will alter their component compositions. Because gas compositions are a function of all gases in a system, a change in the reactive gases will exert influence over the composition of all subsurface gases, including gases that do not participate in biogeochemical reactions.  1.2  Nonreactive Gases  The geochemistry of an aquifer is incomplete without a comprehensive understanding of dissolved gas chemistry. Dissolved gases participate in an array of geochemical and biogeochemical redox reactions. For instance, O2 is commonly consumed during the degradation of organic matter. Conversely, CO2, N2, H2S, and CH4 are produced during biological activity in soils. Dissolved gases, such as noble gases, many CFCs, and SF6, remain conservative throughout the course of all biogeochemical reactions. The 2  application of noble gases in hydrogeological studies has been traditionally dominated by the assumption that noble gas distributions are not affected by biological processes.  Nonreactive gases have been implemented in a variety of groundwater studies, where they are commonly used to determine groundwater residence times (Torgerson et al., 1977; Schlosser et al., 1988), groundwater recharge temperatures (Andrew and Lee, 1979), tracing contaminant gases (Clark et al., 2008), assessing vadose zone gas transport processes (Amos et al., 2005), and detecting the presence of bubbles and the possible ebullition of said bubbles from saturated pore water (Brennwald et al., 2005; Zhou et al., 2005). The nonreactive gases are instrumental in many groundwater investigations because they do not participate in biological reactions.  The nonreactive noble gases are present within the atmosphere at wellestablished values (Andrew and Lee, 1979). In groundwater, contributors to dissolved noble gas signals can include noble gases derived from the mantle and terrigenically derived gas components. Radiogenically derived gases included 3He resulting from tritium decay. Tritium and 3He measurements can be used to determine the age of groundwater in shallow aquifers (Torgersen et al., 1977a).  40  Ar and 21Ne can be  elevated through radiogenic means; however, additions of this nature will generally only become significant in ancient groundwater. In shallow aquifers any change in dissolved noble gas ratios, save 3He/4He, should not deviate significantly from atmospherically equilibrated values.  1.3  Vadose Zone Nonreactive Gas Transport  Reactive gases in the vadose zone link biologically mediated geochemical reactions to vadose zone gas transport. If available electron acceptors have been consumed, the redox state of the system becomes sufficiently low and fermentation and methanogenesis ensue. The resulting biogenic gases will diffuse through the vadose 3  zone along a concentration gradient. The release of CO2 and CH4, as a result of methanogenesis, generates a pressure gradient in the pore space of the sediment away from the methanogenic reaction zone (Amos et al., 2005; Molins and Mayer, 2007).  All gases in the vadose zone will advect towards an area of lower pressure. Provided the CH4 flux tends towards an aerobic zone, CH4 will react with O2 in the presence of methanotrophs. The CH4 oxidation will promote a decrease in total pressure (Amos et al., 2005). Gases in the unsaturated pore spaces will, therefore, advect into the methanotrophic reaction zones.  Inert gas in the vadose zone will be subject to the pressure gradients within the pore space. These nonreactive gases will be enriched in the direction of the net mass flux and depleted in the opposite direction (Thorstenson and Pollock, 1989). Amos et al. (2005) demonstrated that Ar and N2 are enriched in areas of contaminant gas depletion, indicating an advective flux towards the reaction zone. This thesis applies the same principle to noble gases, which, if successful, will infer that noble gases can act as gas transport tracers in the unsaturated pore space of systems undergoing various other biogeochemical reactions, such as denitrification.  1.4  Gas Exsolution and Bubbles in Groundwater  Methanogenesis in the saturated zone will promote gas exsolution, leading to the formation of entrapped gas bubbles. The dissolution of trapped bubbles will not occur unless the sum of the equilibrium partial pressures of all dissolved gases present in solution is less than the total external pressure at the point of dissolution. The total pressure is a function of both the hydrostatic head and the size of the trapped bubble, which is analogous to the inverse of surface tension. Surface tension will dominate bubble formation in fine-grained soils, but its contribution to the total external pressure will diminish with increasing grain size (Kipfer et al., 2002). 4  Dissolved gases in the saturated zone will partition between the groundwater and the gas bubbles. This partitioning is dependent on Henry’s constant, which is a function of temperature. If gas production occurs within the groundwater, the total pressure of dissolved gases will increase. If gas production is sufficient, gas exsolution will ensue and bubbles will form. Gas bubbles will grow in size, and the upward acting buoyancy forces on the bubbles will increase. Large bubbles will reduce the effective permeability of an aquifer and will act as a sink for volatile dissolved components. Degassing will occur in the water surrounding the bubble so long as the bubble exists in a semi-closed system. The bubbles will tend to migrate upwards provided that buoyancy forces overcome the capillary forces. The upward migration of the bubbles is referred to as ebullition.  The processes of gas exsolution and ebullition can be investigated and further substantiated by analyzing inert dissolved gases. Previous studies have established that noble gases will degas into air bubbles based on their respective mass dependent solubilities (Brennwald et al., 2005; Zhou et al., 2005). The lighter noble gases have a higher affinity for the gas phase. If degassing is significant, the results should correlate to previous studies, which cite an enrichment of heavier noble gases relative to lighter gases in the pore water. Furthermore, if the formation and upward migration of a bubble occurs sufficiently fast, isotopic fractionation of a gas will ensue, consistent with Rayleigh fractionation (Brennwald et al., 2005; Zhou et al., 2005). Provided that diffusion of gas in the vadose zone can be assessed, the vadose zone should become enriched in lighter noble gases relative to heavier noble gases, so long as the bubbles pass across the water table.  1.5  Research Questions  The behavior of nonreactive gases in methanogenic environments is the common theme throughout each chapter of this thesis. Below is a list of research questions that embody the relationship between natural attenuation and nonreactive gases. The 5  research questions are presented in a concise and clear manner so that derived conclusions will yield an overall understanding of how nonreactive gases relate to both hydrocarbon contamination in a shallow unconfined aquifer and to ebullition occurring under controlled laboratory conditions. •  Is accurate sampling of vadose zone noble gases possible?  •  Will noble gas component compositions confirm previous findings of gas generation and transport in the vadose zone?  •  Which noble gases are best able to delineate processes in the vadose zone?  •  Can noble gases be used to assess the extent of degassing occurring within the saturated zone of a shallow unconfined aquifer?  •  Are noble gases suitable as tracers for ebullition under shallow aquifer opensystem conditions?  •  To what degree does hydrocarbon contamination alter the effectiveness of an injected nonreactive gas tracer?  •  Can atmospherically derived Ar gas and SF6 gas injectant act as tracers for ebullition under controlled laboratory conditions and what information can be gained from a comparison between the two tracer types?  •  Can ebullition alter gas compositions in the vadose zone of an aquifer?  6  2  2.1  Noble Gases as Transport and Reaction Tracers in the Vadose Zone of a Hydrocarbon Contaminated Shallow Subsurface  Introduction  The successful removal of hydrocarbons from the subsurface is variable and can be arduous because of its dependency on residual hydrocarbon saturation levels. Monitored natural attenuation (MNA) is implemented as a cost-effective alternative to active remediation techniques. The successful remediation of sediments impacted by light non-aqueous phase contaminants is complicated by factors such as: electron acceptor availability, the type of substrate, free phase product viscosity, water table gradients, nutrient availability, and the capillary forces in finer grained soil. The effectiveness of biodegradation can be assessed through a carbon mass balance of the system.  Aerobic biodegradation is the most efficient pathway for the breakdown of organic matter. A decline in the efficiency of hydrocarbon degradation generally correlates to a lowering in the redox state of the system. The lowest redox state, methanogenesis, is established when organic matter itself acts as the electron acceptor. Fermentation and methanogenesis form two additional moles of gas (CO2 and CH4), which, in turn, elevates the mole fraction of biogenic gases in the pore space of the vadose zone. The mole fraction, X i , of a gas is defined by Xi =  ni nT  [3]  where n i is the molar concentration of the gas [mol] in the mixture, and nT is the total number of moles [mol].  Gases migrate along diffusive gradients within the vadose zone of an aquifer. 7  Subsurface diffusion is commonly modeled as single component Fickian diffusion. Fickian diffusion is valid for gases at low partial pressures (Thorstenson and Pollock, 1989); however, as described by the Dusty Gas Model (DGM), to more accurately model subsurface gas transport, in particular in the presence of non-reactive gases, as well as gas generation and consumption, the consideration of multi-component gas diffusion is required (Thorstenson and Pollock, 1989). The DGM couples Knudsen diffusion, multicomponent diffusion, and advection in a series of non-linear equations described by Thorstenson and Pollock (1989), Massmann and Farrier (1992), and Molins and Mayer (2007).  Gas production of an ideal gas in the subsurface leads to an increase in the partial pressure, pi , of that gas at a constant volume, V , and temperature, T [Kelvin], as defined by the ideal gas law (Atkins and de Paula, 2002):  piV = n i RT  [4]  where R is the universal gas constant, commonly reported as 0.082057 L atm K−1 mol−1.  Dalton’s Law dictates that in ideal systems, an increase in the partial pressure of any component gas will increase the total pressure [ P ] of the system. Daltons Law is defined as P = ∑ pi  [5]  The total pressure and the partial pressure of both an ideal and a real gas can be used to calculate the mole fractions of a component gas (Atkins and de Paula, 2002): pi = PX i  [6]  The total pressure in a reaction zone will, therefore, increase at the point of biogenic gas formation, which, in turn will induce a pressure gradient within the subsurface (Amos et al., 2005; Molins and Mayer, 2007). The gases will migrate along 8  the generated pressure gradient with advection acting as the driver behind gas transport. The contaminant gases will also be affected by diffusion. If CH4 enters an aerobic environment, methanotrophic bacteria will oxidize CH4 in a reaction that consumes two moles of gas (CH4 and O2) and produces one mole of gas (CO2), effectively reducing the total pressure. If the subsurface is subject to gas consumption, the ensuing pressure gradient will yield an advective flux into the reaction zone. Gas transport can ultimately lead to gas release from the subsurface (Metcalfe and Farquhar, 1987). Modeling efforts that have focused on advection as a driver for gas transport, include De Visscher et al. (2003), Gaganis et al. (2004), and Molins et al. (2009). The Dusty Gas Model (DGM) was used by Molins and Mayer (2007) to model vadose zone gas transport.  If reaction rates are constant, the system will establish a quasi-steady state. The advective flux of nonreactive gases into the methanotrophic reaction zone results in its enrichment of nonreactive gases (Thorstenson and Pollock, 1989). The consequence of the gas enrichment is that a diffusive flux of nonreactive gases forms back along the advective flux gradient. The total diffusive flux will be equal to the advective flux, but in the opposite direction (Thorstenson and Pollock, 1989). The diffusive flux, however, is not uniform for all nonreactive species because it is dependent on the diffusion coefficients of the individual gas components.  Diffusion coefficients can be calculated as a function of the mass of the molecule in question (Jähne et al., 1987). Lighter molecules travel at a greater rate than heavier molecules, resulting in a relative enrichment of heavier nonreactive molecules in the methanotrophic reaction zone. Noble gases range in mass from 4 AMU to upwards of 136 AMU and have well-established molar atmospheric volumes (Andrews and Lee, 1979) and solubilties (Weiss, 1970, 1971; Weiss and Kyser, 1978; Benson and Krause, 1976). Moreover, noble gases do not participate in biological reactions and, as such, are ideal tracers for diffusive gas transport.  9  Inquiry into current literature suggests that a suite of atmospheric noble gases has yet to be employed as a tool for evaluating vadose zone gas transport; however, noble gases have previously been injected into the vadose zone at elevated levels to investigate partitioning effects (Simon and Brusseau, 2007). Past modeling efforts have centered on Ar and N2 as nonreactive vadose zone gas tracers (Molins et al., 2009). Although valid under specific conditions, N2 is generally considered a reactive gas and can both be consumed and produced during biogeochemical reactions. Alteration of noble gas mole fractions can occur through radiogenic means; however, in a shallow vadose zone, the time scale over which the gases are transported and the proximity to the atmosphere precludes the interference of radiogenic noble gases with the detailed analysis of gas transport principles.  The suitability of noble gases as gas transportation markers in a methanogenic setting is investigated at a crude oil contamination site in Bemidji, Minnesota. Noble gas volumes are collected at vapor ports directly overlying the water table and at two locations where gas profiles are measured as a function of depth beneath the ground surface. An enhanced version of the reactive transport code, MIN3P, is used to evaluate noble gas fluxes and to compare them against past modeling efforts at the site (Molins and Mayer, 2007). This chapter evaluates the accuracy involved with using noble gas tracers as a device to measure vadose zone gas fluxes, in transport regimes significantly impacted by the biogeochemical consumption and production of gas. In addition, this study attempts to identify the noble gases that are the best indicators of biogeochemical reaction sites within the vadose zone, so long as the reaction sites impinge on gas compositions.  2.2  Site Description  In 1979, as a result of a high-pressure underground crude oil pipeline burst, approximately 1.7 x 106 L of crude oil was released into the surrounding environment at a site located 16 km northwest of Bemidji, Minnesota (Figure 2.1). The mean annual 10  temperature at the site is approximately 8 ºC. The water table at the site is 6 m to 9 m beneath the ground surface and annual water table fluctuations average 0.5 m (Amos and Mayer, 2006b). The site is located in a glacial outwash aquifer which consists of sandy gravel, gravely sand, and moderately to poorly sorted sand. Thin sand and silt lenses are identified throughout the site. Moderate amounts of calcium carbonate are present within the sediments and a clayey till is situated approximately 20 m beneath the aquifer (Franzi, 1988). The site vegetation includes primarily tall grass and pine trees. Annual recharge at the site ranges between 10 and 20 cm a year (Herkelrath and Delin, 2001).  Figure 2.1. Bemidji research site location. The figure is based on data presented in USGS (2009).  Initial clean-up efforts resulted in the removal of 1.3 x 106 L of crude oil; however, in and around 4.0 x 105 L of crude oil infiltrated into the subsurface (Hult, 1984). Two distinct oil bodies are present at the site, referred to as the south pool and the north pool (Figure 2.2). Current research efforts focus on wells located along the axis of the 11  north pool. Residual light non-aqueous phase liquid “LNAPL” ranges in depth from near ground surface to the water table at levels from 10% to 20 % (Dillard et al., 1997). The LNAPL in the saturated zone can extend down to 1 m below the water table and is present at saturation levels of 30% to 70% (Dillard et al., 1997). The latest estimate of the crude oil remaining in the north pool LNAPL is 147,000 L (Herkelrath, 1999).  Figure 2.2. Plan view of the Bemidji field site and the locations of the hydrocarbon plumes present at the site. Figure was based on data collected from USGS (2009).  A cross section of the north pool is illustrated in Figure 2.3. BTEX concentrations within the plume, originating from the north pool, have increased, as has the methanogenic zone in the saturated sediments (Cozzarelli et al., 2001). Dissolved CH4 concentrations have been recorded as high as 15 mg L-1 (Cozzarelli et al., 1994). The dissolved CH4 plume is expanding at a rate of 2 to 3 m y-1 (Bekins et al., 2005); however, the average velocity of groundwater at the site is 36.5 to 182 m y-1 (Baedecker et al.,1993). The dissolved CH4 plume geometry is attenuated with respect to the predicted plume geometry (Baedecker et al.,1993). 12  Figure 2.3. A cross section intersecting the extent of the Bemidji site, positioned through the axis of the north plume, detailing the position of the LNAP, and the relevant site geology. Site geology is based on data presented in Smith and Hult (1993).  13  2.3  Vapor Phase Sample Collection and Analysis  The vapor well monitoring network at the Bemidji site is extensive, however only select wells are sampled for noble gases. Well sampling locations are depicted in Figure 2.4. Each vapor well contains between 5 and 9 ports, spanning from the ground surface to just above the capillary fringe. Individual ports consist of 10 cm screens, which are located at 1 m intervals. Each vapor well consists of a stretch of stainless steel tubing, of either 1/8” or 1/4" outer diameter “OD”. Vadose zone gas is pumped to the surface with a peristaltic pump. Sample collection and analysis methods differ for both major component gas analysis (CH4, CO2, O2, and Ar) and noble gas analysis (He, Ne, Ar, Kr, and Xe).  Figure 2.4. A cross section along the axis of the north plume, detailing the position of the vapor wells that are sampled during noble gas analysis, the position of the LNAP, and the relevant site geology.  2.3.1 Major Component Gas Sampling and Analysis  Sampling is conducted at all available vapor wells within the vicinity of the north pool and at background locations. For major component gas analysis, gas is driven from the 14  vadose zone into a Hamilton 10 mL Pressure-Lok® syringe with a peristaltic pump. The syringe is purged once prior to sampling. The sample gas is always kept slightly above atmospheric pressure to prevent the contamination of the sample with ambient gases. The gas is analyzed on site with a Varian CP-4900 dual channel gas chromatograph, which uses He as the carrier gas. Ar, O2, and N2 separation occurs on a Molsieve 5A column and CO2 and CH4 peak separation occurs on a PoraPLOT U column. Ambient air and Supelco vol/vol calibration standards are used to create multipoint calibration curves. Sample gas mole fractions are assessed through the linear regression of sample peak areas.  2.3.2 Vapor Phase Noble Gas Sampling  Twenty vadose zone noble gas samples are analyzed in total. An air sample is collected at the site because it is used to ensure the validity of the analysis method. Eight samples are collected from ports located directly above the water table, including one background sample (310G-1), 6 samples in the source zone, (533G-1, 534G-1, 601G-1, 9014G-1, 9016G-1, and 9017G-1), and 1 sample representative of down gradient conditions (532G-2). The background sample characterizes the native gas compositions, prior to hydrocarbon contamination. The vadose zone lower port wells are sampled so that the vadose zone compositions directly above the water table can be evaluated, at locations both within and down gradient of the source. Noble gas values sampled from these wells will also be implemented as normalization parameters for dissolved concentrations. Additionally, 4 samples are collected at various depths above vapor well 532G-2 (532G-3, 532G-4, 532G-5, and 532G-6), and 7 samples are collected at various depths above vapor well 601G-1 (601G-2, 601G-3, 601G-4, 601G5, 601G-5 DUP, 601G-6, and 601G-7). The samples collected from vapor well 532G are situated just in front of the free phase oil, where as 601G samples are collected from the heart of the source zone. Profile samples are collected to establish an idea of the gas flux within the subsurface, both ahead and within the vicinity of the oil body. Sampling locations are provided in Figure 2.4.1. 15  A hose clamp is used to secure impermeable pump tubing to the vapor well. The tubing is attached to a 1 m long 3/8” copper tube via Swagelok Fittings. The copper tubing is purged for two tube volumes prior to tube closure. A check valve is placed on the outlet end of the copper tube. The downgradient end of the copper tubing is secured using Imperial tube clamps. The upgradient end is quickly sealed with an Imperial tube clamp. Both open ends of the copper tube are pinched with a crimper to prevent leaks during transport.  2.3.3 EAWAG Vapor Phase Noble Gas Analysis  Before the sample gas is analyzed, the copper tube is attached to the end of the noble gas extraction line. The sample is opened and the pressure and temperature of the gas is recorded under closed conditions. The extraction line techniques are based on freezing out principles and inline gettering. Gettering is used to remove all of the reactive gases from the sample. Once this is achieved, Kr and Xe are frozen out of the gas phase through the use of liquid nitrogen, while Ar, Ne, and He are free to travel through open sections of the extraction line. He, Ne, and Ar isotope volumes and ratios are read congruently on an all metal 90° magnetic sector mass spectrometer fitted with a linear Baur-Signer source. Helium volumes are also expanded into a second noncommercial 90° sector mass spectrometer fitted with a double collector system and Baur-Signer source, so that 3He/4He ratios can be assessed. He, Ne, and Ar are pumped out of the system and Kr, and Xe are allowed to expand into the all metal 90° magnetic sector mass spectrometer, where their isotope ratios are assessed. Detailed procedures and instrumentation for noble gas analysis are provided in Beyerle et al. (2000).  16  2.4  Results  2.4.1 Major Gas Vadose Zone Sampling Results  A summary of the major component gas mole fractions sampled throughout the vadose zone of the site is presented in Appendix A. The CH4 concentrations are generally highest in vapor ports closest to the water table. The O2 concentrations are higher at ports nearest the ground surface. O2 values extend through the vadose zone at background concentrations and in vapor wells down gradient of the source zone but rapidly deplete in wells located over the free product. O2 consumption is also evident in wells adjacent to the source zone. CH4 concentrations are near non-detectable levels in wells close to the ground surface and in wells not situated above the LNAPL. CO2 concentrations remain relatively high throughout the vadose zone, with the exception of background wells. The major gas component mole fractions are presented in Appendix A. The CH4 and O2 contours are used to delineate the extent of the methanotrophic zone, which is illustrated in Figure 2.5. The lighter shaded contour in Figure 2.5 indicates that both O2 and CH4 is less than 10% of the total pressure, whereas, the darker shade of grey denotes the region over which both O2 and CH4 drop below 1%.  17  Figure 2.5. A cross section along the axis of the north plume, detailing the position of the vapor wells that are sampled during noble gas analysis, the position of the LNAP, the relevant site geology and the location of the methanotrophic zone. The methanotrophic zone is approximated by contouring O2 and CO2 vadose zone measurements that were obtained with a Varian CP-4900 GC during the 2008 sampling session.  The 2008 dataset shows variations of N2 and Ar values throughout the vadose zone. Enrichments of these gases, in comparison to atmospheric values, is observed in the methanotrophic zone, while depletion of Ar and N2 characterize methanogenic areas, located above the free product. Revesz et al. (1995) detected a substantial decline in Ar and N2 component compositions that correlated to carbon isotope fractionation signatures indicative of CH4 oxidation. Previous gas datasets compiled at the site established that the percent compositions of N2 and Ar were augmented relative to atmospheric vales in the methanotrophic reaction zone and depleted in areas thought to be undergoing methanogenesis (Amos et al., 2005).  18  2.4.2 Noble Gas Vadose Zone Sampling Results  Throughout this chapter, to facilitate comparisons between enrichment and depletion levels relative to atmospheric concentrations, noble gas sample measurements are normalized to atmospheric values. Atmospheric noble gas component compositions have been well documented (Andrews and Lee, 1979), and they are defined in Table 2.1. Noble gas data, as measured by EAWAG noble gas extraction line techniques and mass spectrometry, are summarized in Appendix B. He gas is often omitted from analysis for the reason that its concentrations across the site appear erratic and do not follow the trends consistently observed in the four remaining noble gases. He gas anomalies have also been detected in past gas datasets collected at the site. Several possible processes may contribute to the He anomalies. He gas in soils may be elevated if uranium is present in underlying bedrock (Tindall et al., 2008). He may also have been released from the free product oil. Furthermore, He is extensively used as a carrier gas at the site and as a result, He gas could enter the subsurface through mass transfer between the laminar flow regime and the vadose zone. Finally, tritium decay will generate 3He (Schlosser et al., 1988).  19  Table 2.1. Isotopic composition of atmospheric noble gases (from Andrews, 1979) Vol. % in Atmosphere  Mol % of Element  3  6.8E–10  1.4E0–4  4  He  5.2E–04  100.00  Total He  5.2E–4  He  20  1.7E–03  91.05  21  4.7E–07  0.01  22  1.6E–04  8.94  Ne Ne Ne  Total Ne 36  Ar  38  Ar  40  Ar  Total Ar  1.8E–3 3.2E–03 5.9E–04 9.3E–01  0.33 0.06 99.60  9.3E–1  78  4.0E–07  0.35  80  2.6E–06  2.27  82  1.3E–05  11.56  83  1.3E–05  11.55  84  6.5E–05  56.90  86  2.0E–05  17.37  Kr Kr Kr Kr Kr Kr  Total Kr  1.1E–4  124  Xe  8.3E-09  0.01  126  Xe  7.7E-09  0.09  128  Xe  1.7E-07  1.92  129  Xe  2.3E-06  26.44  130  Xe  3.5E-07  4.08  131  Xe  1.8E-06  21.18  132  Xe  2.3E-06  26.89  134  Xe  9.0E-07  10.44  136  Xe  7.6E-07  8.89  Total Xe  8.6E-6 20  The normalized vadose zone sample measurements are presented in Figure 2.6. Sampled Bemidji air corresponds well to atmospheric levels. The noble gas component compositions of the source zone wells (601-1, 534G-1, 9014-1, 9016-1, and 9017-2) are significantly depleted relative to atmospheric compositions. Additionally, a significant enrichment of noble gases occurs in wells 532-3, 532-4, and 601-4. Also, background well 310G-1 is slightly enriched with noble gases.  Figure 2.6. Vadose zone noble gas volume fractions normalized to atmospheric values sampled from vapor wells located along the axis of the north plume. Atmospheric values are delineated by the straight line intersecting the graph.  2.4.3 Method Comparison  Ar mole fractions are analyzed with both the major component gas analysis method 21  “GC” as well as with the noble gas analysis method “EAWAG”. Normalized Ar values, as measured by each analysis method, are compared in Figure 2.7 at each individual well. The Ar and N2 values obtained through GC calculations were subject to peak manipulations because of column contamination. The GC dataset however, corresponds to previous annual gas values obtained at the site and to results analyzed by a distinct set of measurements recorded by the United States Geological Survey “USGS” during the 2008 sampling event. Ar values, as measured by both methods, trend together and, moreover, the Ar values reside within the bounds of experimental error for the majority of the vapor wells. The largest divergence between the datasets occurs in the percent compositions found at wells 601-1, 601-5, and 532-4. The two methods of analysis yield values that coincide and, therefore, both methods appear valid. Ergo, comparisons of gas components collected between different analysis methods are justifiable.  Atm  Figure 2.7. A side by side comparison of vadose zone argon gas volume fractions sampled from vapor wells located along the axis of the north plume, measured with a Varian 4900 GC or by the EAWAG methods.  22  2.5  Discussion  2.5.1 Total Pressure Variations in the Reaction Zones  It can be argued that pressure fluctuations within the subsurface can explain the observed enrichment and depletion patterns. Noble gas samples obtained from vapor ports situated within the methanogenic reaction zone could potentially be depleted as a result of an increase in total pressure. The opposite also holds true for gas compositions determined from sample ports located in the methanotrophic reaction zone above the water table. An increase in mole fraction as a result of a universal pressure change to all component gases would incite a pressure change of equal magnitude among each noble gas. Pressure fluctuations at the Bemidji site have previously been evaluated through modeling efforts conducted by Molins et al. (2009). Modeling results indicate that the total pressure fluctuations within the subsurface are minor in comparison to the degree of observed noble gas depletion or enrichment. Simulated subsurface pressure fluctuations are presented in Figure 2.8. A 0.2 atm pressure increase would insight a 2% error in the noble gas measurements. The actual noble gas values range from 10 to 20% of normalized atmospheric gas compositions. Therefore, the variations in observed noble gas values should be in response to vadose zone gas transport processes.  23  Figure 2.8. A cross section along the axis of the north plume detailing the simulated gas pressures as % deviation from atmospheric levels. Shaded areas indicate zone of elevated (dark) and lowered (light) pressure. The figure is modified from (Molins et al., 2009).  2.5.2 Background Conditions  The noble gases sampled from the background vapor well, 310G-1, are statistically greater than atmospheric values. At depths proximal to the water table the water vapor, and possibly CO2, will be elevated relative to atmospheric gas volumes. An increase in the total number of gas molecules of a single component augments the partial pressure of said component in the pore space, which culminates in an increase in the total pressure and a decrease in the nonreactive gas partial pressures. On the other hand, the consumption of O2 within the subsurface causes the total pressure to decline. Water table fluctuations may also alter total subsurface pressures. Generally, dissolved noble gas concentrations in groundwater tend to be higher than theoretical values (Heaton and Vogel, 1981), in a phenomenon, commonly referred to in the noble gas community as excess air. The concept of excess air is further evaluated in Chapter 3. The enrichment of vadose zone noble gases at the background location may be explained by the repartitioning of excess air from the saturated zone into the overlying vadose 24  zone by diffusion or due to a change in the water table elevations.  2.5.3 Elemental Ratio Analysis  The elemental ratios of noble gases, normalized to atmospheric ratios, are used to assess the influence of diffusion over the system. Gases travel as an equimolar flux when advection is the driver for gas transport; however when the operative is diffusion, a mass-dependent elemental fractionation will be present among the gases. Noble gas ratios are presented in Figure 2.9.  Figure 2.9. Vadose zone noble gas volume fraction ratios normalized to atmospheric values sampled from vapor wells located along the axis of the north plume. Atmospheric values are delineated by the straight line intersecting the graph.  25  The ratios are depleted in the midlevel wells 532-3, 532-4, 532-6, 533-1, and 601-4. These wells are situated within the methanotrophic reactions zones. This result suggests that heavier noble gases are enriched relative to lighter noble gases in the methanotrophic reactions zones. This observation can be explained by the fact that lighter noble gases are more able to escape via diffusion.  In methanogenic source zone vapor ports, lighter noble gases are enriched relative to heavier gases in wells 534-1, 601-1, 9014-1, and 9016-1. Gas advects upwards from areas of gas production. Advection will be countered by a diffusive downward flux towards the methanogenic zone. The diffusion of lighter gases will be faster than heavier gases, which provides reason for their relative enrichment in this area. Furthermore, the diffusion gradient between the methanotrophic zone and the methanogenic zone is more pronounced, as it is bound by the water table and not replenished by atmospheric gases. An increase in lighter gases in the methanogenic reaction zone could also be affected by the partitioning of heavier gases into the free phase oil. The opposite noble gas signal is observed in the pore water, suggesting that the oil is saturated with noble gases, and has little influence over gas volumes. The potential for oil partitioning of noble gases is investigated further in Chapter 3. Elevated noble gas ratios could also result from the ebullition of gases. This prospect is investigated further in both Chapters 3 and 5. For the scope of this Chapter all noble gas ratios are assumed to represent flow within the unsaturated zone.  2.5.4 Temperature Effects  The transfer of heat through the vadose zone is dependent on the water content, the type of soil, and the degree of soil compaction (Tindall et al., 2008). The thermal conductivity (ability of a material to transfer heat along a temperature gradient) and the soil diffusivity are used to calculate heat flow; however, these values can be quite variable in nature. Seasonal temperature fluctuations are evaluated in the sandy soil subsurface of a Canadian pine forest, south of permafrost regions. Diurnal temperature 26  fluctuations recorded in the vadose zone penetrated no more than 1 m from ground surface. Seasonal temperature differences could be detected as deep as 6 m within the subsurface; however, the greatest variations were recorded between a 2 m interval extending down from the ground surface (Tindall et al., 2008). Temperature deviations diminish with depth. At depths greater than 2 m, the change in temperature ranges within a few degrees. Heat flow will alter gas transport within the vadose zone at Bemidji but it is only expected to have a significant impact at depths shallower than 2 m. A change in temperature will also influence gas solublities. Heavier gases partition into the pore water more readily than lighter gases. The solubility of lighter gases is also more easily influenced by temperature. For the purposes of this thesis, this effect is considered negligible at a depth greater than 2 m below the ground surface.  2.5.5 Noble Gas Profiles  Two noble gas profiles are sampled at the site. The first profile analyzed is situated along vapor well 601, located within the centre of the oil body. This location is proximal to the smear zone, where residual levels of oil contaminate the vadose zone as a result of the vertical migration of oil through the subsurface, prior to oil reaching the water table. The conceptual model assumes that the system is one-dimensional “1D” and that horizontal fluxes will not impact modeled gas fluxes. This simplification of the system ignores the impact horizontal gas flow will have on the system, as a result of residual oil present within the smear zone. Past modeling efforts have successfully modeled vapor well 601 as a 1D system (Amos et al., 2005, Molins and Mayer, 2007). The conceptual model at vapor well 601, simplified in Figure 2.11, suggests that nonreactive gases will advect into the methanotrophic zone and diffuse out of the zone, along the advection gradients (Amos et al., 2005).  27  Figure 2.10. Conceptual model applied to vadose zone noble gas transport at vapor well 601.  The second profile to be assessed is situated on the leading edge of the methanotrophic zone, at ports positioned down well 532G. CH4 concentrations verge on non-detectable levels at this well, although O2 noticeably decreases with depth, from 20% to 10%. The conceptual model (Figure 2.11) at this well is simply that noble gases are transported into the area of O2 consumption through advection and back to the surface by diffusion.  28  Figure 2.11. Conceptual model applied to vadose zone noble gas transport at vapor well 532.  The noble gas percent compositions, normalized to atmospheric values, recorded along profiles at 601 and 532G are presented in Figure 2.12 and Figure 2.13, respectively. The Ar dataset at vapor well 601 corresponds to past Ar profiles modeled at the site (Molins and Mayer, 2007). At 601, the midlevel ports are enriched with noble gases. The midlevel ports are situated within the methanotrophic zone, which implies a flux of all gases into the area of gas consumption. CH4 oxidation generally occurs throughout the length of vapor well 532G. This assumption correlates well to the observed increase in noble gas volumes along that profile. Additionally, the lower ports are enriched with lighter gases relative to heavier gases while the mid level ports show an enrichment of heavier noble gases relative to lighter gases. The elemental fractionation signals observed at both profiles confirms the supposition that changes to gas mole fractions are not just a function of a pressure change, but are likely 29  representative of transport processes.  Figure 2.12. A profile plotted with depth of vadose zone noble gas volume fractions normalized to atmospheric values at vapor well 601. Atmospheric values are delineated by the straight line intersecting the graph.  30  Figure 2.13. A profile plotted with depth of vadose zone noble gas volume fractions normalized to atmospheric values at vapor well 532. Atmospheric values are delineated by the straight line intersecting the graph.  Noble gas ratios recorded at profile 601 and 532G are presented in Figure 2.14 and Figure 2.15, respectively. At 601, the depletion of the heavier gases is greatest at the lowest monitoring points, and the greatest depletion is seen among the heavier noble gases. The depletion pattern also appears to be mass dependent. Enhanced diffusion of lighter gases away from the methanotrophic zone could provide reason for such a pattern. Vapor well 532G indicates an enrichment of heavier gases with depth, evidence of the relatively slow diffusion of heavier gases relative to lighter gases. Note that transport processes occurring above the methanotrophic zone behave as an open system, with molecules free to exit the system along the ground surface boundary. Below the methanotrophic reaction zone, the gases will behave as a semi-closed system, as they are bound by the water table.  31  Figure 2.14. A profile plotted with depth of vadose zone noble gas volume fraction ratios normalized to atmospheric values at vapor well 601. Atmospheric values are delineated by the straight line intersecting the graph.  32  Figure 2.15. A profile plotted with depth of vadose zone noble gas volume fraction ratios normalized to atmospheric values at vapor well 532. Atmospheric values are delineated by the straight line intersecting the graph.  2.6  MIN3P-DGM Noble Gas Migration Model  2.6.1 The Dusty Gas Model  Previously, the Dusty Gas Model (DGM) of diffusion was incorporated into a version of the reactive transport model MIN3P code (Molins and Mayer, 2007). The DGM is based on the coupling of multi-component diffusion with a nonequimolar flux of gas, opposed to the more commonly modeled single component diffusion, which is expressed by Fickian gas transport, N iD [mol m-2 s-1]. The diffusion of each gas is driven through differences in partial pressures. Fick’s law treats the transport of each gas separately and is defined in terms of partial pressures: 33  N iD = Dij ∇Ci =  Dij ∇pi RT  [7]  where Dij [m2 s-1] is effective molecular diffusion coefficient i of in j.  Fickian equations only account for single component diffusion. Multi-component flow of an ideal gas can be described by the Stefan-Maxwell approximation. A key assumption of the Stefan-Maxwell approximation is that molecular diffusion is the key component to flow. In the Stefan-Maxwell equation all resistance to flow originates from the interaction with other molecules. The effect of flow on diffusion induced from total pressure gradients is assumed to be negligible. Additionally, the Stefan-Maxwell approximation is only valid over a limited range of permeabilities (Thorstenson and Pollock, 1989).  The DGM combines multi-component diffusion with the Knudsen’s diffusion to present a more complete approximation of gas transport. Knudsen’s diffusion is the dominant diffusion mechanism in a system where the pore size is sufficiently low or the total pressure is sufficiently low so that molecules only collide with pore/capillary walls. With the DGM, the individual fluxes associated with each species in a mixture are independent and thus are additive; the momentum change in the system is additive and proportional to the change in the number of molecules of the system.  During multi-component transport, a light molecule will have a higher thermal velocity causing a non-equimolar flux within the system. This non-equimolar flux is the difference between the total diffusive flux and the molecular flux of species i (effects of concentration gradients). The non-equimolar flux for a species is related to the mole fraction of that species in the system, relative to a stationary set of coordinates, and thus, is dependent on the total amount of species in the system at that point. Simply speaking, the non-equimolar flux represents a bulk gas flux. The full derivation if the 34  DGM can be found in Thorstenson and Pollock (1989), Massmann and Farrier (1992), and Molins and Mayer (2007).  The transport equation is used to model the change in a system through time. The transport equation for the system in steady state is d(CX i ) + ∇(N iT ) = 0 dt  [8]  where N iT [mol m-2 s-1] is the total molar gas flux of i relative to a fixed coordinate system. The transport equation can be solved using various methods, such as, the finite difference method, the finite element method, or the finite volume method. The flux is solved for every component in the mixture between two points in the system as it moves with time.  2.6.2 Model Parameters  The DGM version of the reactive transport code, MIN3P, is implemented in the vadose zone modeling. MIN3P uses the finite volume method. The model domain is one dimensional, along the z-axis, The grid is equally divided into 40 cells. Boundary conditions are imposed on half cells, positioned outside of the model domain. The model is run for 2315 days representing quasi-steady state conditions. Previous model runs of a more simplistic system have suggested that the system reaches steady state within 3 years (Molins and Mayer, 2007).  The major component gases and noble gases are used to calibrate the hydrocarbon degradation rate entered into the model. The MIN3P-DGM code has previously been used to match the major component gas profiles to the actual gas component compositions that were measured in the field, at vapor well 601 (Molins and Mayer, 2007). The initial input file for profile 601 was based off the input file described 35  in Molins and Mayer (2007). Various constants, associated with noble gas transport, were added to the database of the reactive transport code. The Henry’s constants for noble gases, obtained from datasets compiled from Benson and Krause (1976), were entered into the model database at both 10 ºC and 25 ºC. Both sets of Henry’s constants are included in the database for the reason that the component composition profiles calculated by Molins and Mayer (2007) pertained to gas fluxes within standard temperature regimes; however, final modeling efforts focused on transport occurring at 10 ºC. Table 2.2 summarizes the log (model stipulation) of the Henry’s constant values implemented in solubility calculations during MIN3P modeling efforts.  Table 2.2. Henry’s constant values added to the MIN3P-DGM database Gas Species  Log KH (atm M-1) (10°C)  Log KH (atm M-1) (25°C)  Source  He  3.3929  3.4070  Benson and Krause (1976)  Ne  3.2956  3.3394  Benson and Krause (1976)  Ar  2.7304  2.8539  Benson and Krause (1976)  Kr  2.4414  2.3590  Benson and Krause (1976)  Xe  2.1625  2.8980  Benson and Krause (1976)  N2  3.0696  3.1798  10°C = Benson and Krause (1976)  O2  2.7681  2.8980  10°C = Benson and Krause (1976)  CO2  1.2833  1.4736  10°C = Sander (1999)  CH4  2.7227  2.8894  10°C = Sander (1999)  Additional constants entered into the model include Lennard Jones potentials and gas viscosities. The Lennard Jones potential expresses the energy involved with molecular interactions as a function of distance. The two parameters required to estimate the Lennard Jones potential associated with a molecule are the variables rho (ρ) and epsilon (ε), which are calculated from data provided in Reid et al. (1997). Gas viscosities must also be specified in the input file. The gas viscosities are calculated through a variety of equations, found in various different sources for individual gas components. The equations used to calculate viscosity are summarized in the cited 36  references. The Lennard Jones parameters and the viscosities for gas components are specified in Table 2.3.  Table 2.3. Gas viscosities and Lennard-Jones potentals specified in the input file implemented in MIN3P-DGM transport modeling Gas  Wilke Viscosities (ηi)  Source  Lennard-Jones (ρ/ε)  Source  O2  2.00e-5  Molins et al., 2009  3.4678/106  Molins et al., 2009  CO2  1.00e-5  Molins et al., 2009  3.758/148.6  Molins et al., 2009  CH4  1.40e-5  Molins et al., 2009  3.941/195.2  Molins et al., 2009  He  1.80e-5  Green, 2008  2.551/10.22  Reid et al., 1997  Ne  3.15e-5  Geankoplis, 1972  2.820/32.8  Reid et al., 1997  Ar  2.2e-5  Green, 2008  3.542/93.3  Reid et al., 1997  Kr  2.56e-5  Lide, 2004  3.655/178.9  Reid et al., 1997  Xe  2.2e-5  Green, 2008  4.047/231.0  Reid et al., 1997  N2  1.70e-5  Molins et al., 2009  3.798/71.4  Molins et al., 2009  The theoretical parameters that are associated with a gas are generally well defined; whereas, the physical properties describing the aquifer can be subject to heterogeneities and can exist over a wide range of values. Constants related to the aquifer are compiled from both past field data experiments and modeling efforts conducted at the Bemidji site. Literature data used for model calibration is summarized in Table 2.4.  37  Table 2.4. Literature parameters for physical aquifer attributes at the Bemidji site Parameter  Literature Values  Porosity (volume void/volume media)  0.38 (Essaid et al., 1995)  Recharge Rate (m y-1)  range 0.26-0.54 (Dillard et al., 1997) 0.1 - 0.2 (Herkelrath and Delin, 2001) 0.2 – 0.3 (Herkelrath and Delin, 2001)  Vertical Hydraulic Conductivity  10-5 m s-1 (Essaid et al., 1995)  Van Genuchten, alpha (m^-1)  0.77 – 9.34 (Dillard et al., 1997)  Van Genuchten, n  1.77 – 11.88 (Dillard et al., 1997)  Residual Saturation  0.05 (Molins, 2007)  Modifications to the Molins and Mayer (2007) input file included changing the boundary conditions. The original input conditions consisted of an upper and lower constant head flow boundary. The upper boundary is changed to a flux boundary, corresponding to the average groundwater recharge at the site. The gas mole fractions, system mass balance, hydraulic head, pressure head, gas and water saturations, and calculated flux values were compared. The differences between a model using a flux boundary and a model with an imposed constant head boundary were deemed negligible. A flux boundary, corresponding to recharge, is imposed on all following vadose zone simulations. The lower flow boundary remains unchanged from initial input parameters, and it is expressed as the negative distance from the lowest measurement point to the water table. The right and left flow boundaries are impermeable.  A constant concentration boundary is imposed on the upper level cells. Other modifications to the initial input file include changing the concentrations associated with that boundary. The initial input file had gas concentrations inputted as partial pressures, which were later converted to constant concentrations during model calculations. The concentrations in this paper are expressed as the dissolved concentrations associated with the partial pressure at the point of gas entry into the model domain. Furthermore, the domain is extended up to the ground surface. The domain size is estimated from 38  the water level information provided in Table 2.5. The gas ports used to calibrate component compositions are spaced evenly every 1 m, extending down from the ground surface. A second type free exit reactive transport boundary is applied along the bottom of the model domain.  Table 2.5. Profile port locations with depth Well  Oil level  Surface  Port 1  Port Interval  601  423.5  431.78  431.28  7 at 1 m  532  423.5  432.34  431.84  7 at 1 m  Calibrated amounts of CH4 and CO2 are added to the model at the bottom of the domain to represent the methanogenic biodegradation in the smear zone. The source term is applied to the lower 5 cm of the domain. The rate at which CH4 and CO2 is added to the system is used to calibrate system fluxes. Throughout model calibration, it became evident that permeability changes to the system were required to refine gas component compositions.  2.6.3 601 Model Results  So long as a constant temperature is kept throughout the entire model domain, the gas mole fraction profiles between two simulations of different temperatures are identical. The results of two simulations, each with temperatures fixed across the domain at either 25 °C or 10 °C, are compared. A change in temperature at depth from ground surface will generate a slight shift in the gas mole fractions (not shown). The following simulations assume a constant temperature throughout the domain.  Two simulations of varying porosities and hydraulic conductivities are carried out at profile 601 for the reason that noble gas calibration accuracy is dependent on the fine-tuning of aquifer properties; major component gas profiles calibrated well to 39  modeled concentrations at various aquifer property settings. Simulation 1 models gas flow through a homogeneous domain. The porosities and hydraulic conductivities in the lower 3 m of the domain are varied in simulation 2, in order to account for a possible lower permeability layer at the site. A summary of the simulation parameters is presented in Table 2.6.  Table 2.6. Assigned aquifer property variables at profile 601 implemented in the MIN3P-DGM modeling Aquifer Property  Simulation 1  Simulation 2  Porosity  0.38  0.38 / 0.33  K (m s-1) from 0-3 m  5.0 x 10-5  5.0 x 10-5  K (m s-1) from 3-6.55 m  5.0 x 10-5  3.0 x 10-6  Van Genuchten, alpha (m-1)  3.00  3.00  Van Genuchten, n  1.60  1.60  Residual Saturation -1 -1  0.05 -8  0.05 -6  -9  CH4 Rate (mol l s )  2.3 x 10 (1.15 x 10 )*  6.0 x 10 (3.00 x 10-7)*  CO2 Rate (mol l-1s-1)  1.7 x 10-8 (8.50 x 10-7)*  4.0 x 10-9 (2.00 x 10-7)*  *Rate expressed as a flux in mol m-2 s-1  2.6.4 MIN3P- DGM Discussion for Profile 601 Biogenic gas production rates are estimated through model calibration. The degree of fit that simulated gas values exhibit towards measured component compositions is maximized during calibration. The higher porosity simulation (simulation 1) requires the larger biogenic gas production rate (Table 2.6). The rate of methane gas generation for simulation 1 is 1.15 x 10-6 mol m-2 s-1. This corresponds well to previous vadose zone MIN3P modeling data at the site, which approximates the rate of methane generation at 1.5 x 10-6 mol m-2 s-1. These rates are in excess of the 8.1 x 10-7 mol m-2 s-1 estimate, provided by Chaplin et al., (2002). Gas production associated with the layered heterogeneous model domain (simulation 2) imparts a much lower CH4 generation rate 40  (3.00 x 10-7 mol m-2 s-1), yet it yields a better fit between the actual concentrations, and the modeled values. The difference in the modeling rates suggests that permeability of the system will substantially alter subsurface gas profiles. It also suggests that past estimates at the site may have overestimated the actual rate of gas production, and that noble gas data is required to further constrain the system fluxes. The modeled major component gases, coupled with field measurements, at vapor well 601, are plotted with respect to depth in Figure 2.16, and noble gas values are defined in Figure 2.17.  Figure A  Figure B  Figure 2.16. Vertical profiles of modeling results and field measurements for major component gas mole fractions at vapor well 601. Figure A illustrates modeling results of a homogenous subsurface. Figure B illustrates modeling results for a layered heterogeneous subsurface with a lower permeability layer in the lower portion of the domain.  41  Figure A  Figure B  Figure 2.17. Vertical profiles of modeling results and field measurements for noble gas mole fractions at vapor well 601. Figure A illustrates modeling results of a homogenous subsurface. Figure B illustrates modeling results for a layered heterogeneous subsurface, with a lower permeability layer in the lower portion of the domain.  Results infer that reactive transport models based on the DGM of multi-component diffusion can accurately predict noble gas mole fractions within the vadose zone of an aquifer. The results also suggest that a lower permeable layer is present in the subsurface. An unconformity is indicated in the borehole log characterizing an adjacent monitoring well (Appendix C). Inaccuracies in the gas profiles may be ramifications of errors in the permeability estimations or in the soil moisture content profiles. The sediments nearer the water table likely have an elevated water content level; whereas, dryer conditions probably dominate near ground surface locations. It is also possible that the residual oil contamination, present in the soil at well 601, reduces aquifer permeability. Additionally, methanotrophic bacterial reactions can yield extracellular substances, which can also lower aquifer permeability (Wilshusen et al. 2004).  42  Aquifer properties must be constrained so that accurate biogenic gas production rates can be determined (Table 2.6). Noble gases are enriched, as stipulated by the DGM, in the methanotrophic zone. Heavier noble gases are depleted relative to lighter gases in the methanogenic zone, which could insinuate that partitioning of the noble gases into the oil may alter measurements at lower ports. Overall, noble gas profiles can be accurately modeled with the MIN3P-DGM code; moreover, the simulated gas profiles confirm that the largest signals of depletion or enrichment are detected among the heavier gases.  Gas fluxes for simulation 2 at profile 601 are presented in Figure 2.18. O2, CH4, CO2, Ne and Xe flux values are displayed spatially in units of moles per day. A larger zone of high permeability medium will increase the flux of non-reactive gases through the subsurface (not shown). Advection is compared against the DGM of multicomponent diffusion, which inherently accounts for the nonequimolar flux. The nonequimolar flux, as well as Fickian diffusion, are presented for informational purposes.  43  Advection Diffusion DGM Nonequi  Figure 2.18. Vertical profiles of the advective, diffusive, non-equimolar and DGM flux at vapor well 601 for a layered heerogeneous system, with a lower permeability strata in the lower portion of the domain. Plots illustrate system fluxes for O2, CH4, CO2, Ne, and Xe, respectively. O2 is transported into the reaction zone primarily by diffusion, at which point it is completely consumed. The advective flux of O2 is comparably much lower than the diffusive flux. The primary transport mechanism behind the flow of CH4 is upwards diffusion, with a diffusive flux that is much larger than the associated advective flux. The upward transport of CO2 is via advection; however, as the pressure gradient begins to subside, the CO2 continues to diffuse upwards.  44  Profiles at 601 indicate that noble gases can act as key markers for diffusion because the diffusion of noble gases is mass dependent. Ne values suggest that the Fickian diffusion differs from the DGM multicomponent diffusive flux. A proportion of the total Ne flux can be attributed to a nonequimolar flux. Xe results, however, suggest that Fickian diffusion is equal to multicomponent diffusion, although advection in the system must still be considered. A much smaller nonequimolar flux is associated with Xe. Results suggest that nonreactive gases are transported into the methanogenic zone by advection and exit this zone by diffusion. This corresponds to results obtained for the Ar and N2 modeling efforts of Molins and Mayer (2007). Results also suggest the difference between diffusion and the DGM are largest above the water table. Noble gas ratios confirm that Xe is depleted to a much greater degree than Ne in this area.  2.6.5 532 Model Results  A single permeability simulation is conducted at vapor well 532. The aquifer properties implemented in the modeling of gas transport at well 532 are similar to those used in the simulations at profile 601. The parameter values are summarized in Table 2.7.  Table 2.7. Assigned aquifer property variables at profile 532 implemented in MIN3P-DGM modeling Aquifer Properties  Simulation 1  Porosity  0.38  K (m s-1) from 0-3 m  5.0 x 10-5  Van Genuchten, alpha (m-1)  3.00  Van Genuchten, n  1.60  Residual Saturation  0.05  CH4 Rate (mol l-1s-1)  1.5 x 10-8 (7.50 x 10-8)*  CO2 Rate (mol l-1s-1)  9 x 10-10 (4.50 x 10-8)*  *Total Amount Per m2 45  2.6.6 MIN3P-DGM Discussion for Profile 532  The measured major gas profiles and noble gas profiles of well 532, along with the simulated profiles, are presented in Figure 2.19 and Figure 2.20, respectively. The DGM model can accurately simulate the major component gas and noble gas profiles. Calibration efforts suggest that large He discrepancies occur at well 532. He discrepancies are common at the Bemidji site, and thus are omitted from analysis for the reasons described on page 16. The vadose zone at 532 is enriched in noble gases, suggesting that gas consumption as a result of methanotrophic reactions occurs throughout the vadose zone in locations upgradient of the plume, but in a more diffuse manner. The noble gas values do not exhibit large deviations along the extent of the profile; however, Xe clearly becomes progressively enriched with depth in comparison to atmospheric values, because diffusion of Xe out of the system is slower than diffusion of its lighter counterparts. The rate at which gases are added to the model domain is much less than that of 601. The model neglects horizontal flow within the aquifer from the source zone, which may explain discrepancies between the actual and model results.  Figure 2.19. Vertical profile of modeling results and field measurements for major component gas mole fractions at vapor well 532, in a homogenous subsurface. 46  Figure 2.20. Vertical profile of modeling results and field measurements for noble gas mole fractions at vapor well 532 in a homogenous subsurface.  At vapor well 532, the CH4 and CO2 gases are transported upwards, towards the ground surface. CH4 is consumed prior to exiting the vadose zone; CO2 is not inhibited within the vadose zone and freely exits the porous sediment. The O2 is a precursor for CH4 consumption; it travels from the atmosphere into the vadose zone by diffusion. The transport processes are outlined in Figure 2.21. Diffusion accounts for the bulk transport of all reactive gases. Although diffusion is the major component of the total system flux, the advective flux is sufficient enough to promote movement among the nonreactive gases. A downward advective flux of the nonreactive gases is opposed by an upward diffusive gradient in all instances. The simulated noble gas profiles agree with the noble gas profiles of 601 in that the diffusive flux for Xe equals the DGM of multicomponent diffusion. For both profile locations, differences are evident between the two types of diffusive flux when lighter nonreactive gases are concerned because 47  the lighter noble gases constitute a larger proportion of the nonequimolar flux. Advection Diffusion DGM Nonequil  Figure 2.21. Vertical profiles of the advective, diffusive, non-equimolar and DGM flux at vapor well 532. Plots illustrate system fluxes for O2, CH4, CO2, Ne, and Xe, respectively.  2.7  Conclusions  A clear methanotrophic zone is delineated in the vadose zone by a measured enrichment of noble gases, which is consistent with the conceptual model. Noble gases are depleted relative to atmospheric levels in methanogenic source zone ports, directly 48  above the water table, for the reason that the nonreactive gases advect away from the area of biogenic gas production. The flux of noble gases through the subsurface can be accurately predicted with the MIN3P-DGM code. Model calibration is dependent on both inherent aquifer properties and on the biogenic gas production rates. Mass fractionation is observed during gas transport, whereby the heavier noble gases exhibit a more enhanced signal in areas of gas consumption and gas generation. The diffusion of heavier gases out of the reaction zone is much slower than its lighter counterparts. Overall, Xe and Kr are the most sensitive noble gas tracers for reactive transport studies in the vadose zone. Noble gases help to constrain model input parameters and can be used to estimate biogenic gas production rates or relative aquifer permeability, porosity, and moisture content, in the presence of gas flow.  49  3  Dissolved Noble Gas Concentrations as Tools to Evaluate Degassing and Ebullition in Hydrocarbon Contaminated Settings  3.1  Introduction  The success of natural attenuation is highly dependent on the rate of consumption of hydrocarbon molecules, which, intern, is a function of both the native site conditions and the redox state of the system. In extremely reduced conditions, anaerobic respiration ensues and microbes known as methanogens thrive. During the terminal stage of organic matter decay, larger carbon chains will undergo fermentation, whereby endogenous reactions cede smaller organic molecules. At this redox state, CO2 is also able to act as an electron acceptor. Methanogens derive energy from the breakdown of the small organic molecules in a process known as methanogenesis. The byproducts of degradation, CH4 and CO2, are both detected in significant concentrations in the saturated zone of the Bemidji aquifer (Bekins et al., 2005).  At the Bemidji site, modeling results suggest that the dissolved CH4 plume is attenuated (Amos et al., 2005). One possible explanation for CH4 attenuation is degassing (Ryan et al., 2000), which refers to the formation of gas bubbles in saturated sediment as result of dissolved gas over-pressuring. Dissolved CH4 gas, as well as other dissolved volatile species found in the pore water, partition into gas bubbles based on Henry’s Law, which states that the amount of gas contained within the dissolved phase is proportional to the amount of gas present in the vapor phase. The solubility of a noble gas is therefore, dependent on the partial pressure of the gas in the vapor phase and is related to the dissolved concentration through Henry’s constant ( k H ): kH =  Ci pi  [9]  50  Traditionally, during noble gas analysis the dissolved concentrations of noble gases are measured directly. The dissolved concentrations are used to estimate corresponding vadose zone partial pressures. Equilibria of dissolved gas concentrations with partial pressures vary with both temperature and salinity; however, for the purposes of this study, the salinity effect is negligible due to the dilute nature of the groundwater at the site.  Henry’s Law can also be reported in terms of gas mole fractions through the relationship (Sander, 1999) k Hpx =  pi 55.3 = Xi kH  [10]  The dimensionless form of Henry’s constant ( k Hx ), measured as the number of moles in the gas phase over the number of moles in the water phase, can be approximated by (Sander, 1999) 1/k Hx = k H RT  [11]  Dissolved noble gas concentrations are commonly reported in units of cm3(STP) g-1. The conversion to Henry’s Law in units of cm3(STP) g-1 (Kipfer et al., 2002) is k HSTP = k Hx  T Po ρ w To  [12]  where Po is standard pressure, To is standard temperature, and ρ w is the density of water (approximated at 1 g cm-3).  The elevation above sea level of a measuring point will affect the amount of atmospheric gas that is able to dissolve into the water. Atmospheric pressure generally 51  decreases with elevation. Total pressure changes with elevation can be approximated by (Kipfer et al., 2002) P=p e sl  −h hs  [13]  where, h is the altitude [m], hs is the scale height and p sl is the pressure at sea level. The partial pressure of a gas is a function of the total pressure. The actual average pressure during the sampling period at the Bemidji site is 0.95 atm. The total amount of gas that dissolves into the groundwater will, therefore, be less than it would otherwise be at lower elevations. This approximation must be considered when calculating dissolved gas concentrations from measured mole fractions. The gas composition in the vadose zone might vary from atmospheric levels as a result of biogeochemical reactions, so knowledge gained from vadose zone transport processes must be understood prior to calculating dissolved concentrations.  The consumption and production of gases is not limited to the vadose zone and will also occur beneath the water table. If CH4 comes into contact with O2, it will undergo CH4 oxidation. However, the carbon isotope fractionation signal along the flow path is not typical of CH4 oxidation (Revesz et al., 1995), suggesting the unlikelihood that CH4 oxidation is occurring in the saturated pore water. Possible explanations for premature CH4 loss in the saturated zone include: dispersive mixing, LNAPL isolation of the source zone (Essaid et al., 1995, 2003), air partitioning as a result of water table fluctuations (Fry et al., 1995; Williams and Oostrom, 2000), LNAPL partitioning, and finally, influence over transport processes as a result of native heterogeneities inherent within the aquifer (Harvey and Gorelick, 2000).  All of the above postulates have merit; however, physical evidence at the site supports the theory of gas exsolution, and gas bubble formation leading to the possibility of ebullition. A core sample extracted in the vicinity of vapor well 9014, at elevations between 421.3 m and 423.5 m has an abundance of entrapped gas bubbles 52  held within the sediment (Amos et al., 2005). Cores recovered from the source zone at two different times are presented in Figure 3.1. The difference between the two cores could insinuate that degassing is increasing with time, as the plume tends to a more reduced state. Bubble tracts can also be seen in the far right core, which would suggest that ebullition could act as a mechanism for carbon escape from the subsurface.  Figure 3.1. Core sample recovered from the source zone of the Bemidji site. The figure is adapted from Amos et al. (2005). The core samples on the left and centre left were recovered from the vicinity of vapor well 9014, at a depth intervals 421.3 m to 423.5 m. The core samples on the right were recovered in 1997 from the vicinity of monitoring well 421. The diameter of each core is 47 mm.  Investigations into the extent of carbon mass loss from the saturated zone as a result of degassing and ebullition is accomplished through the analysis of dissolved inert gases, in particular noble gases. Noble gases will partition into bubbles based on their respective solubilities. As a whole, it is expected that the dissolved concentrations of noble gases become depleted with gas exsolution. The partitioning of noble gases between the dissolved phase and gas bubbles will result in a solubility-based fractionation, whereby lighter noble gases and noble gas isotopes will escape a liquid phase more readily than their heavier counterparts (Brennwald et al., 2005; Zhou et al., 2005). Figure 3.2 outlines the conceptual model behind the processes involved with 53  dissolved noble gas partitioning behavior in the presence of bubbles. The overall outcome will be an enrichment of heavier gas molecules relative to lighter gas molecules in the pore water and, conversely, an enrichment of lighter gas molecules relative to heavier gas molecules in the unsaturated zone, so long as the gas bubbles cross the water table.  Figure 3.2. Conceptual model applied to dissolved noble gas transport in the saturated zone of the highly methanogenic sediment at the Bemidji site.  For this work, dissolved noble gas concentrations will be collected from the saturated zone of the Bemidji site (see Chapter 2 for site description). Sampling locations are chosen based on previous evidence of the occurrence of degassing and possible ebullition processes. Conceptual modeling will be used in an attempt to distinguish an ebullition signal from a degassing signal in the dissolved pore water.  54  3.2  Dissolved Gas Sample Collection and Analysis  Samples are collected in monitoring wells located: within the source zone (315, 534B, 533B), at depth (533C), at background conditions located up-gradient of the hydrocarbon contamination (310E), and, finally, in wells located down-gradient of the free phase oil (532A); i.e., within the groundwater plume. In Figure 3.3 the sampling locations are depicted along the axis of the north pool.  Figure 3.3. A cross section along the axis of the north plume detailing the position of the vapor wells and monitoring well that are sampled during noble gas analysis, the position of the LNAPL, and the relevant site geology.  3.2.1 Dissolved Noble Gas Sampling  The monitoring wells sampled for noble gases are purged for a minimum of 3 well volumes with a positive displacement pump. The purged water is collected in a large tub to prevent contaminated water from re-infiltrating the subsurface. The pump tubing is fastened to a 1 m long 3/8” copper tube with gastight Swagelok fittings. The copper 55  tube is placed in a custom wooden frame to prevent bending during sampling. Two Imperial tube clamps are secured within the wooden frame. The tube clamps are fitted with ¼” washers and nuts to facilitate tight closures. During sampling, the pump hose is closely inspected for the presence of bubbles. No bubbles were visually detected during any sampling events. The tube clamp located farthest from the pump is tightened fully during sampling. The second tube clamp is immediately closed. The sampling method ensures that at all times the water is over pressured, which eliminates the possibility of air contamination. Noble gas analysis was conducted at EAWAG Noble Gas Laboratory according to the procedure detailed in (Beyerle et al., 2000).  Figure 3.4. In field photograph of a noble gas water sample and sampling apparatus, collected for noble gas analysis at EAWAG.  3.2.2 EAWAG Dissolved Noble Gas Analysis  Copper tubes are accurately weighed, the water in the tubes is then expanded into an evacuated headspace vessel, which is shaken vigorously for a period of approximately 15 mins. The gases initially dissolved in the water partition between the water and the headspace volume. The headspace gas is expanded into a noble gas extraction line, which is under high vacuum. The extraction line techniques and mass spectrometry procedures are identical to those outlines in section 2.3.3. 56  3.3  Results  Table 3.1 summarizes the Henry’s constants for each noble gas as k Hpx [atm (mol mol1 -1  ) ], k H [(mol L-1) atm-1], k Hx [dimensionless], and k HSTP [atm cm-3(STP)L-1]. The  tabulated Henry’s constants are calculated at a temperature of 10 ºC, a pressure of 1 atm and at 0 ‰ salinity. All constants are based on data found in Benson and Krause (1976).  Table 3.1. Henry’s coefficients for noble gases at 10°C at 1 atm and 0 ‰ salinity, and manipulation thereof. All values are calculated from data collected in Benson and Krause (1976) Gas  k Hpx  kH  k Hx  k HSTP  He  1.37E+05  4.03E-04  1.07E+02  1.11E+02  Ne  1.10E+05  5.04E-04  8.56E+01  8.56E+01  Ar  2.99E+04  1.85E-03  2.33E+01  2.33E+01  Kr  1.54E+04  3.59E-03  1.20E+01  1.20E+01  Xe  8.08E+03  6.84E-03  6.31E+00  6.31E+00  The noble gas array calculated at each well is compared against a specified dissolved concentration, particular to each gas, so that analysis of all five gases can be carried out simultaneously, and so that the relative change of each gas can be expressed as a percentage of the selected normalization parameter. The noble gases are compared against dissolved atmospheric concentrations, background concentrations, and to the overlying vadose zone conditions. For this approach to be valid, the normalization parameters must all be expressed in the same units as the dissolved gases. In Table 3.2, the vadose zone concentrations and atmospheric values are converted to dissolved concentrations, tabulated in units of cm-3(STP) g-1 and mol L-1. Monitoring wells that are normalized to overlying vadose zone conditions are done so by pairing the monitoring well with the nearest vapor port, or to the vapor port that is most representative of the overlying conditions. For reference purposes, raw data results are provided in Appendix D. 57  Table 3.2. Vadose zone mole fractions converted to dissolved concentrations for paired vadose zone – saturated zone wells at the Bemidji site Paired Gas V.Z. pi Err (atm) Theoretical Err Theoretical Err M.W V.W (atm) S.Z (cc g-1) (cc cc-1) S.Z (mol L-1) (cc cc-1) Air He 4.98E-06 4.48E-08 2.00E-09 n/a Ne 1.73E-05 2.02E-07 8.72E-09 Ar 8.87E-03 3.80E-04 1.64E-06 Kr 1.08E-06 9.01E-08 3.89E-10 Xe 8.17E-08 1.30E-08 5.59E-10 310-1 He 5.38E-06 6.E-08 4.60E-08 5.E-10 2.07E-09 2.E-11 310E Ne 1.90E-05 2.E-07 2.11E-07 3.E-09 9.12E-09 1.E-10 531E Ar 9.69E-03 2.E-04 3.95E-04 7.E-06 1.71E-06 3.E-08 533C Kr 1.19E-06 3.E-08 9.41E-08 3.E-09 4.10E-10 1.E-11 Xe 9.23E-08 6.E-09 1.39E-08 9.E-10 6.05E-10 4.E-11 4.48E-08 1.E-10 4.51E-08 1.E-10 532A 532-2 He 5.24E-06 2.E-08 Ne 1.79E-05 4.E-08 1.99E-07 5.E-10 1.54E-07 4.E-10 Ar 9.49E-03 5.E-05 3.86E-04 2.E-06 8.18E-05 4.E-07 Kr 1.19E-06 3.E-08 9.16E-08 1.E-09 9.98E-09 1.E-10 Xe 9.23E-08 6.E-09 1.30E-08 5.E-10 7.42E-10 3.E-11 533-1 He 5.45E-06 9.E-08 4.66E-08 8.E-10 4.69E-08 8.E-10 533B Ne 1.89E-05 1.E-07 2.10E-07 2.E-09 1.63E-07 1.E-09 Ar 9.68E-03 9.E-05 3.94E-04 4.E-06 8.34E-05 8.E-07 Kr 1.23E-06 2.E-08 9.76E-08 2.E-09 1.06E-08 2.E-10 Xe 9.42E-08 4.E-09 1.42E-08 7.E-10 8.12E-10 4.E-11 534-1 He 5.09E-06 3.E-08 4.35E-08 2.E-10 4.38E-08 2.E-10 534B Ne 1.68E-05 7.E-08 1.87E-07 8.E-10 1.45E-07 6.E-10 Ar 8.21E-03 5.E-05 3.34E-04 2.E-06 7.07E-05 5.E-07 Kr 9.64E-07 1.E-08 7.62E-08 1.E-09 8.31E-09 1.E-10 Xe 7.02E-08 3.E-09 1.06E-08 4.E-10 6.05E-10 2.E-11 9016 He 5.15E-06 1.E-08 4.41E-08 1.E-10 4.44E-08 1.E-10 315 Ne 1.75E-05 4.E-08 1.94E-07 4.E-10 1.51E-07 3.E-10 Ar Kr Xe  8.60E-03 1.02E-06 6.97E-08  2.E-05 6.E-08 2.E-09  3.50E-04 8.06E-08 1.05E-08  9.E-07 5.E-09 3.E-10  7.41E-05 8.79E-09 6.00E-10  2.E-07 6.E-10 2.E-11  58  The measured noble gas data, normalized to atmospheric values, is summarized in Table 3.3. The difference between the dissolved and atmospheric concentrations, exhibited in Figure 3.5, represents the extent to which noble gases stray from their initial well-defined atmospheric concentrations. For this reason, the dissolved atmospheric concentrations are not corrected for moist air. The figure represents the combined influence of vadose zone and saturated zone gas transport and partitioning processes over noble gas concentrations. Clearly, from Figure 3.5, the noble gas fractions at the site deviate significantly from atmospheric values at all wells save the background well (310). The largest divergences of noble gases from atmospheric conditions are found at the source zone wells 534B, 315, as well as the down gradient well 532A. The He data collected at the wells is erratic, but has been included into the analysis for completeness.  Table 3.3. Dissolved noble gas concentrations normalized to the atmospheric dissolved noble gas concentrations at monitoring wells positioned along the axis of the plume of the north pool at the Bemidji site Monitoring Well He/Heatm Err. He/Heatm Ne/Neatm Err. Ne/Neatm Ar/Aratm Err. Ar/Aratm Kr/Kratm Err. Kr/Kratm Xe/Xeatm Err. Xe/Xeatm  310E 0.93  531A 1.81  532A 0.26  533C 0.78  533B 2.13  534B 0.49  315 0.27  0.02  0.03  0.00  0.01  0.04  0.01  0.00  0.89  1.35  0.22  0.76  0.71  0.37  0.21  0.02  0.02  0.00  0.01  0.01  0.00  0.00  1.02  0.79  0.43  0.98  0.81  0.52  0.24  0.02  0.01  0.00  0.02  0.01  0.01  0.00  1.02  0.70  0.51  1.00  0.80  0.58  0.53  0.03  0.01  0.01  0.03  0.02  0.01  0.05  1.05  0.66  0.65  1.08  0.90  0.71  0.64  0.07  0.03  0.03  0.07  0.05  0.03  0.03  59  Figure 3.5. Dissolved noble gas concentrations in units of cm3(STP)/g normalized to theoretical dissolved noble gas concentrations associated with atmospheric gas sampled from monitoring wells located along the axis of the north plume. Atmospheric values are delineated by the straight line intersecting the graph.  Deviations in the dissolved noble gas concentrations, with respect to measured background concentrations, are presented in Figure 3.6. Results are summarized in Table 3.4. Background values differ from the dissolved noble gases in the source zone and at down gradient locations. Analyzing changes to the dissolved gases along the flow path does not account for vadose zone transport processes occurring within the subsurface, but it does provide insight into the degree of gas stripping along the axis of the plume, and at locations with depth. Anomalies appear at the down gradient well 531A, where He and Ne values are in excess of background values. At this location, the vadose zone gas distributions can generally be characterized by atmospheric compositions. The elevated values are likely the result of air contamination in the sample. The water within the source zone is stripped of gas, inferring that gas 60  exsolution is significant, whereas, only the lighter molecules in 533C (deep well) are depleted, when compared against background conditions. The largest amount of gas exsolution is found at monitoring well 315.  Table 3.4. Dissolved noble gas concentrations normalized to the background dissolved concentrations at monitoring well positioned along the axis of the plume of the north pool at the Bemidji site Monitoring Well  310E  531A  532A  533C  533B  534B  315  He/Heback  1.00  1.94  0.27  0.84  2.32  0.50  0.28  Err. He/Heback  0.02  0.03  0.00  0.01  0.03  0.01  0.00  Ne/Neback  1.00  1.51  0.24  0.86  0.79  0.37  0.21  Err. Ne/Neback  0.01  0.01  0.00  0.01  0.01  0.00  0.00  Ar/Arback  1.00  0.77  0.42  0.96  0.80  0.43  0.20  Err. Ar/Arback  0.01  0.01  0.00  0.01  0.01  0.00  0.00  Kr/Krback  1.00  0.69  0.49  0.98  0.82  0.46  0.45  Err. Kr/Krback  0.02  0.01  0.01  0.02  0.01  0.01  0.01  Xe/Xeback  1.00  0.63  0.58  1.03  0.88  0.52  0.46  Err. Xe/Xeback  0.03  0.02  0.02  0.03  0.02  0.01  0.01  61  Figure 3.6. Dissolved noble gas concentrations in units of cm3(STP)/g normalized to background concentrations (MW 310), sampled from monitoring wells located along the axis of the north plume. Background values are delineated by the straight line intersecting the graph.  A true assessment of ebullition within the source zone can only be achieved if the dissolved concentrations are segregated from changes to gas partial pressures occurring within the subsurface, as a result of gas transport. To accomplish this separation, the noble gas ratios are normalized to the dissolved partial pressures at the lower most vadose zone port nearest the dissolved well. The results are summarized in Table 3.5.  62  Table 3.5. Dissolved noble gas concentrations normalized to the paired vadose zone dissolved noble gas concentrations at monitoring wells positioned along the axis of the plume of the north pool at the Bemidji site Monitoring Well  310E  531A  532A  533C  533B  534B  315  He/Hevadose  0.92  1.79  0.260  0.779  2.11  0.484  0.266  Err. He/Hevadose  0.02  0.03  0.001  0.009  0.04  0.005  0.003  Ne/Nevadose  0.92  1.39  0.230  0.79  0.732  0.381  0.211  Err. Ne/Nevadose  0.02  0.03  0.002  0.01  0.008  0.004  0.002  Ar/Arvadose  1.05  0.81  0.446  1.01  0.838  0.532  0.242  Err. Ar/Arvadose  0.02  0.01  0.004  0.02  0.010  0.006  0.002  Kr/Krvadose  1.03  0.71  0.519  1.01  0.81  0.59  0.54  Err. Kr/Krvadose  0.03  0.01  0.009  0.03  0.02  0.01  0.05  Xe/Xevadose  1.1  0.7  0.7  1.1  0.9  0.7  0.7  Err. Xe/Xevadose  0.2  0.1  0.1  0.2  0.2  0.2  0.2  (Ne/Xe)/(Ne/Xe) vadose  0.8  2.0  0.3  0.7  0.8  0.5  0.3  Err. (Ne/Xe)/(Ne/Xe) vadose  0.2  0.4  0.1  0.1  0.2  0.1  0.1  (Ar/Xe)/(Ar/Xe) vadose  1.0  1.2  0.7  0.9  0.9  0.7  0.4  Err. (Ar/Xe)/(Ar/Xe) vadose  0.2  0.2  0.1  0.2  0.2  0.2  0.1  (Ne/Kr)/(Ne/Kr) vadose  0.89  1.96  0.444  0.78  0.90  0.65  0.39  Err. (Ne/Kr)/(Ne/Kr) vadose  0.03  0.05  0.009  0.02  0.02  0.01  0.04  (Ar/Kr)/(Ar/Kr) vadose  1.02  1.15  0.86  1.00  1.03  0.90  0.45  Err. (Ar/Kr)/(Ar/Kr) vadose  0.04  0.03  0.02  0.03  0.02  0.02  0.04  • Subscript “vadose” indicates overlying partial pressures converted to dissolved concentrations.  Figure 3.7 shows that gases in the source zone are not in equilibrium with overlying vadose zone concentrations, suggesting that significant degassing, and possibly ebullition, is occurring faster than diffusion and advection can replenish the gases in solution. Partitioning into hydrocarbons is also considered minimal, as it would preferentially retain heavier noble gases relative to lighter gases. The opposite signal is observed. 63  Figure 3.7. Dissolved noble gas concentrations in units of cm3(STP)/g normalized to theoretical dissolved noble gas concentrations associated with overlying vadose zone gas volume fractions sampled from monitoring wells located along the axis of the north plume. Vadose zone values are delineated by the straight line intersecting the graph.  The dissolved noble gases measured at background well, 310E, and deep well, 533C, correspond well to the assumed vadose zone partial pressures; however, Ne and He dissolved concentrations are depleted by approximately 8%. The heavier noble gases, Ar, Kr, and Xe, are used as indicators for degassing as a result of CH4 overpressuring. They are not as subject to variability as are He and Ne as a result of their lower diffusion coefficients. The normalized noble gas volumes at well 533B are indicative of slight degassing. 533B is screened at a deeper depth than the other source zone wells. The largest degassing volumes are associated with the source zone wells 315, 534B, as well as the down gradient well 532A. Depletion of heavier noble gases and enrichment of lighter noble gases is found at the downstream well 531A. The increase in lighter noble gases at this well is likely the result of air contamination.  64  3.4  Discussion  3.4.1 Kinetic Fractionation  Assuming ebullition is occurring at the Bemidji site, one of two processes will dominate the partitioning behavior of dissolved gases. If the bubble is retained within the sediment, the gases between the bubble and the dissolved pore water will be in equilibrium with each other. On the other hand, if a bubble escapes from the pore water faster than the rate at which it takes noble gases to reach solubility equilibrium, isotopic fractionation of a noble gas will result. Research by Holocher et al. (2002) suggests that bubbles reach an equilibrium with gases dissolved in the pore water within a few hours. Kinetically controlled ebullition in the San Juan coal bed basin was previously negated by Zhou et al. (2005), where the gases were determined to enter a trapped gas phase through the equilibration of pore water with the bubbles. Furthermore, Brennwald et al. (2005) concluded that ebullition of gases in lake sediments did not correspond to kinetic fractionation principles but was instead solubility controlled. It is hypothesized that degassing of dissolved noble gases at the Bemidji site occurs under solubility controls, however, kinetic fractionation calculations are conducted to confirm this conjecture.  The kinetic fractionation signature will depend on the diffusion coefficient of each volatile species in solution (Brennwald et al., 2005; Zhou et al., 2005). The lighter species will diffuse across the gas-water interface faster than its heavier counterparts. The diffusion coefficient of a gas is proportional to the square root of its reduced mass (Jähne et al., 1987). The measured isotopic ratios are presented in Table 3.6 and the normalized isotopic ratios are displayed in Figure 3.8.  65  Table 3.6. Dissolved noble gas isotopic ratios measured at monitoring wells along the plume axis of the north pool at the Bemidji site He/4He  Err.  JK310E  1.96E-06  3.80E-08  1.03E-01  3.15E-04  3.00E+02  2.53E+00  JK531A  1.42E-06  1.61E-08  1.02E-01  2.50E-04  2.97E+02  1.47E+00  JK532A  1.48E-06  4.75E-08  1.03E-01  1.38E-03  2.94E+02  2.86E+00  JK533C  1.97E-06  3.43E-08  1.02E-01  3.85E-04  2.98E+02  2.03E+00  JK533B  6.90E-07  9.24E-09  1.03E-01  3.62E-04  2.96E+02  1.12E+00  JK534B  1.43E-06  3.53E-08  1.01E-01  6.86E-04  2.94E+02  3.07E+00  JK315  1.40E-06  4.15E-08  1.02E-01  1.03E-03  3.04E+02  1.61E+01  Well  3  20  Ne/22Ne  Err.  36  Ar/40Ar  Err.  Figure 3.8. Dissolved noble gas 22Ne/20Ne ratios and 40Ar/36Ar ratios sampled from monitoring wells located along the axis of the north plume.  No apparent trends are detected with the dissolved isotopic ratios measured at the Bemidji site. The 2oNe/22Ne ratios vary between 0.101 ± 0.001 and 0.103 ± 0.001; the 66  40  Ar/36Ar ratios range from 294 ± 3 and 300 ± 20. The isotopic 22Ne/20Ne and 40Ar/36Ar  ratios in air are 0.094 and 290.6, respectively. The values are compared against background ratios for Rayleigh calculations, as all values appear to deviate a consistent amount from atmospheric ratios. The extent of possible kinetic fractionation can be assessed through the Rayleigh fractionation model, the driver behind which is mass dependent diffusion. The model is based on Fick’s Law and assumes that a decrease in concentration over a fixed time interval is equal to the diffusion coefficient, Di , multiplied by the concentration Ci (Brennwald, 2005). Over a fixed unit of time, the decline in concentration of species A, over the depletion in concentration of species B, can be approximated by dCA DA CA = dCB DB CB  [14]  Where: A = species 1 (eg. 36Ne) B = species 2 (eg. 40Ne) Upon integration, the Rayleigh equation becomes: CA  CA  =  f CB  CB  o  DA −1 DB  [15]  with the fractionation term ( f ) expressed as f =  CB CB,o  [16]  Brennwald et al. (2005) manipulated the Rayleigh equation so that two functions could be expressed simultaneously by substituting a fractionation ratio into the original Rayleigh equation:  67  CB CB DB f B CB ,o C −1 = = D = f D DD C C fD D B,o CD,o CD,o  [17]  4 = Species 4 (22Ne is approximated as species 4 in fractionation calculations) Therefore,  DB  f B = f D  DD   −1 +1   [18]  CA  CA   DB −1 DA −1+ DA −1 =   f D  DD  DB   DB  CB  CB  o  [19]  CC  CC   DC −1 =   f D  DD  CD  CD  o  [20]  and  For calculation purposes, species A= 36Ar, species B = 40Ar, species C = 20Ne, and species D = 22Ne.  The isotopic diffusion coefficient of a noble gas can be approximated by the mass of the molecule (Jähne, et al., 1987): M i* =  Mi Mb Mi + Mb  [21]  * Where, M i is the reduced mass; M i is the mass of the species; and M b is the mass of  the medium. Diffusion coefficients are easily calculated, by assuming that the mass of the medium tends to ∞ (Zhou et al., 2005), and so the reduced mass approaches the actual mass.  68  The diffusion coefficients are used to approximate fractionation at the site. No fractionation is assumed to occur at background conditions, because little degassing happens at this well and ebullition is very unlikely to take place at the Bemidji site in the absence of hydrocarbon contamination. A Rayleigh fractionation line is calculated for 22  Ne, with fractionation values varying between 100% (background concentrations) and  an arbitrary value of 50%. The ratios determined for the fractionation line at the defined fractionation values are presented in Table 3.7. Figure 3.9 compares the measured 20  Ne/22Ne and 36Ar/40Ar ratios against the calculated Rayleigh fractionation line.  Table 3.7. Rayleigh fractionation line calculations using fractionation for the defined isotope ratios 3 20 F He/4He line Ne/22Ne line  22  Ne associated  36  Ar/40Ar line  1  1.96E-06  9.76E+00  3.34E-03  0.5  1.52E-06  9.43E+00  3.25E-03  69  Figure 3.9. Dissolved 20Ne/22Ne ratios plotted against dissolved 36Ar/40Ar sampled from monitoring wells located along the axis of the north plume and the site specific Rayleigh fractionation line calculated at fractionation values of 1 and 0.5 as determined by theoretical 22Ne values.  From Figure 3.9, fractionation of noble gases at the Bemidji site is not kinetically controlled. The alternative to a diffusively controlled regime is that noble gas partitioning reaches equilibrium between the gas and pore water, prior to bubble rise. The noble gas depletion signatures are, therefore, solubility controlled.  3.4.2 He Data  He data is omitted from the aforementioned fractionation section because dissolved 3  He/4He ratios deviate from atmospheric concentrations as a result of tritium decay.  Tritium will undergo beta decay and yield 3He. Tritium can be used to empirically date groundwater so long as the groundwater is relatively young and not subject to radiogenic fluctuations. In the 1950s and early 1960s, nuclear tests resulted in the 70  accumulation of tritium to the atmosphere. The largest atmospheric additions of tritium occurred in 1962. The tritium in the atmosphere has significantly decreased since the early 60s. Generally, groundwater that entered the ground prior to the 1940s is assumed to be tritium free. If the water infiltrated the subsurface after it was exposed to atmospheric tritium, larger 3He/4He ratios will infer relatively older water. The 3He/4He ratios at both the background well (310E) and at downgradient well 533C are identical. 533C should have an overall lighter He composition, as it is the deepest well. Diffusion of the lighter He isotope into the methanogenic area from the underlying clean water might provide reason for background He ratios equaling deep well ratios. Ratios from 531A and 533B are neglected, as it appears that they exhibit abnormally high 4He concentrations (Figure 3.7). The 3He/4He ratios at source zone wells are investigated to ensure that they do not conform to kinetic fractionation principles. The mass difference between He isotopes is large and therefore fractionation will also be large. If He is indicative of kinetic fractionation, it would suggest that degassing across the site is comparable. A fractionation line is calculated between 3He/4He and 20Ne/22Ne for 22Ne. Calculations are presented in Table 3.7. From Figure 3.11, it is evident that the He signal is not the result of kinetic fractionation in the source zone.  310E  531A  532A  533C  533B  534B  315  Figure 3.10. Dissolved 3He/4He ratios sampled from monitoring wells located along the axis of the north plume. 71  Figure 3.11. Dissolved 20Ne/22Ne ratios plotted against dissolved 3He/4He,sampled from monitoring wells located along the axis of the north plume and the site specific Rayleigh fractionation line, calculated at fractionation values of 1 and 0.5 as determined by theoretical 22Ne values.  3.4.3 Solubility Controlled Fractionation  The comparison of lighter noble gases relative to heavier noble gases across the site facilitates an empirical assessment of degassing as a result of solubility controls using elemental ratio analysis. All ratios are normalized to the overlying vadose zone conditions to account for discrepancies in gas partial pressures at the point of groundwater infiltration. The solubility ratios of background well 310 are within the range of theoretically determined dissolved concentrations. The elemental ratios, sampled from all source zone wells, indicate significant gas exsolution through solubility dominated mass fractionation processes. Figure 3.12 illustrates that the largest amount of degassing occurs in the source zone wells. The ratios are normalized to the dissolved vadose zone concentrations, to account for vadose zone gas transport 72  processes occurring at the site. The vadose zone partial pressures decrease in the source area; therefore, the low solubility ratios will be accentuated if normalized against atmospheric partial pressures.  Figure 3.12. Dissolved noble gas ratios normalized to theoretical dissolved noble gas concentrations associated with dissolved overlying vadose zone gas volume fractions sampled from monitoring wells located along the axis of the north plume. Vadose zone values are delineated by the straight line intersecting the graph.  3.4.4 Partitioning of Gases into Oil  Noble gases are more soluble in oil than in water. As previously mentioned, the solubility of noble gases in water increases with decreasing mass number; however, the opposite holds true for oil-water partitioning. Heavier noble gases will partition from water into oil more readily than lighter noble gases (Pinti and Bernard,1995; Kharaka and Specht, 1988). Noble gas ratios clearly indicate an enrichment of heavier gases in source zone wells relative to lighter noble gases. The presented noble gases are all 73  normalized to overlying vadose zone conditions. The wells are located near the water table and, as such, the sample water is assumed to mostly originate from percolation through the vadose zone. Dissolved concentrations are heavier than theoretical values; therefore, if oil partitioning is occurring, it is merely dampening the degassing signal observed in the wells. The LNAPL has been exposed to atmospheric conditions for up to 30 years; ergo, it is logical to conclude the free product oil is in equilibrium with its surroundings. The influence of hydrocarbon partitioning on noble gas dissolved concentrations is assumed to be negligible for the scope of this thesis.  3.4.5 Excess Air  Trapped parcels of air are regularly located directly under the water table, brought about by water table fluctuations. Water table fluctuations at the site range up to 0.5 m in amplitude. The dissolved noble gas concentrations in shallow groundwater are a function of the overlying vadose zone gas partial pressures and subsurface temperatures. In groundwater, Heaton and Vogel (1981) report that the measured dissolved gas concentrations are greater than those predicted through Henry’s Law, a phenomenon referred to commonly as “excess air”. The normalized dissolved concentrations at 310E, as well as the elemental fractionation pattern, can most likely be attributed to excess air.  Typical excess air values can range between 10% and 20% of the pore space (Kipfer et al., 2002) at locations adjacent to the water table. The dissolved gases will re-equilibrate between the gas in the bubble trapped under the water table and the pore water. The atmosphere is the only source for both 20Ne and 22Ne, so the excess air in solution can be approximated by comparing the actual 20Ne/22Ne ratio with the theoretical 20Ne/22Ne as predicted by Ne solubility. In the literature, two models are able to account for the observed differences in dissolved concentrations: the partial reequilibration model (Stute, et al., 1995) and the closed system equilibration model  74  (Aeschbach-Hertig et al., 2000). The latter model is commonly accepted as the most accurate model.  The partial re-equilibration model relies on the principles of molecular diffusion. It assumes that the dissolved gases will diffuse across the water table into the unsaturated zone. The diffusion of a noble gas is mass dependent: lighter gases will diffuse quicker than heavier gases. This relationship will prompt an enrichment of heavier noble gases in the saturated zone, as well as isotopic fractionation of a noble gas. The closed system equilibration model assumes that a bubble partially dissolves in water and that it compresses with increasing hydrostatic pressure. The partial dissolution causes a slight enrichment of heavier noble gases in the saturated zone; however, it will not produce isotopic fractionation, as it is primarily reliant on noble gas solubilities. In source zone wells, the production of biogenic gas could potentially offset the probability that entrapped gas bubbles partially dissolve. The presence of excess air is therefore not considered for source zone wells. Note that background conditions indicate enrichment of vadose zone noble gases relative to atmospheric gases.  A possible explanation for the observed excess air values might be related to vadose zone gas transport processes, as described in Chapter 2. Subsurface gas consumption generates a net inwards flux of gas, which leads to an increase in nonreactive gas partial pressures in the areas of gas consumption. Background vadose zone well 310 noble gas values are elevated with respect to atmospheric levels (Figure 2.6). Figure 3.7 suggests that only He and Ne (the gases most susceptible to transport via diffusion) significantly differ from vadose zone conditions. To attain accurate noble gas partial pressures for gas partitioning calculations in shallow unconfined aquifer settings, the vadose zone conditions should be analyzed.  75  3.4.6 Diffusion of Noble Gas in Pore Water and Dissolved Noble Gas Replenishment – Empirical Findings  Noble gas analysis establishes that lighter noble gases are depleted relative to heavier gases at monitoring well 533C, which is located under the saturated methanogenic reaction zone (Bekins et al., 2001). Nothing indicates that gas bubble formation has occurred at 533C, as it is a relatively deep monitoring well. The signal could represent the molecular diffusion of noble gases, originating from the clean groundwater positioned under the CH4 plume into the reaction zone. The diffusion coefficient for all dissolved gases in the pore water is summarized in Table 3.8. Figure 3.13 illustrates a weak correlation between diffusion coefficients and noble gas dissolved concentrations at well 533C. The molecules with the largest diffusion coefficients are also the molecules that exhibit the largest degree of depletion. The water in the source zone might, therefore, be replenished by diffusion of gases from uncontaminated areas of the aquifer.  Table 3.8. Calculated diffusion coefficients of dissolved gases in solution at 10°C Species  *HCO3  **N2  *H+1  *CH4  *CH2O  **He  **Ne  **Ar  **Kr  **Xe  Diff. Co.  1.185  2.00  9.311  1.84  1.089  5.360  2.74  2.50  1.07  0.83  (10-5cm2 s-1) * Values provided by Amos (2006) ** Values calculated from information provided by Jähne et al. (1987)  76  Figure 3.13. Dissolved noble gas concentrations at 533C in units of cm3(STP)/g normalized to background concentrations as a function of each respective diffusion coefficients at 10°C, as estimated from Jähne et al. (1987).  3.4.7 Groundwater Mixing as a Result of Advection- Empirical Findings  The evolution of the plume along the flow path is investigated by comparing the dissolved concentrations found in monitoring wells 310E, 315, 534B, 532A, and 531A, all of which are screened within 1 m of the water table. The distance from each well to the centre of the oil body is summarized in Table 3.9. The noble gas volumes are plotted along the axis of the north plume for shallow monitoring wells in Figure 3.14. The dissolved noble gas concentrations are normalized to the background concentrations sampled at well 310. Figure 3.14 illustrates that Xe exhibits a correlation between dissolved concentrations and distance along the flow path. Dissolved noble gas volumes along the flow path will be complicated by the variability in the extent of degassing occurring at each well. If groundwater recharge is not considered, depletion in noble gas concentrations will occur with distance along the flow path, as bubbles act as sinks for the gases, so long as degassing is ongoing or ebullition is occurring. The 77  heavier noble gases (Kr and Xe) tend to increase with distance from the centre of the plume body, all the while remaining slightly below atmospheric levels. The reason for this is most likely that recharge water replenishes the groundwater. The lighter gases will be preferentially removed from the water phase. The extent of degassing will decrease at distances away from the plume, and the gases originating from recharge water down gradient of the oil body will undergo less gas exsolution.  Table 3.9. Monitoring well construction data coupled with estimates of methanogen counts as approximated by the most probably number technique Well  Top of Screen Elevation (m)  Bottom of Screen Elevation (m)  Distance from 0 Along Vertical Transect (m)  *Approx. log MPN per g Sediment  310E  423.18  421.86  -198  n/a  315  424.68  423.16  -6  4  534B  422.92  422.77  25  1.5  533B  421.80  421.65  35  1.5  533C  420.30  420.14  38  n/a  532A  423.82  422.53  46  2.5  531A  423.70  423.70  67  n/a  **Approximated from Bekins et al. (2005).  78  Figure 3.14. Dissolved noble gas concentrations measured in units of cm3(STP)/g normalized to background concentrations (MW 310) sampled from monitoring wells screened at similar depths located along the axis of the north plume. Background values are delineated by the straight line intersecting the graph.  3.4.8 Relating Dissolved Concentrations to Methanogens  The spatial variability of methanogens at the Bemidji site has previously been characterized using the “Most Probable Number” (MPN) bacterial culture technique in Bekins et al. (2005). MPN counts were collected from various locations at the Bemidji site at shallow depths, along the axis of the plume. The MPN counts are plotted against distance from the center of the oil body (Figure 3.15). Estimates of MPN counts are summarized in Table 3.9.  79  Figure 3.15. The log MPN counts of methanogens per g of saturated sediment plotted against along the axis of the north plume, modified from Bekins et al. (2005).  In Figure 3.16 the estimated MPN counts are plotted against the normalized Ar/Kr ratios for monitoring wells located within the source zone (315, 534B, 533B, and 532A). The smallest elemental ratios correspond to the largest MPN counts at the site. The largest amount of degassing (smallest elemental ratio) occurs at well 315 and correspondingly, the highest MPN counts are also found in the vicinity of 315. The observed degassing at well 534B is less than the assumed gas exsolution measured at wells located both up and downgradient of 534B. This result correlates well to the low MPN count detected within the vicinity of 534B. Both the variability in MPN counts and the dissolved noble gas ratios suggest that gas production in the source zone is subject to local variability within the subsurface, which can be attributed to inherent site heterogeneities.  80  Figure 3.16. Ar/Kr ratios of source zone wells normalized to theoretical dissolved noble gas concentrations associated with overlying vadose zone gas volume fractions as a function of MPN methanogen count, as reported by Bekins et al. (2005).  An additional study by Bekins et al. (2001) plots MPN counts as a function of depth. The methanogen estimates are used to approximate the location of a methanogenic zone, illustrated in Figure 3.17. Two distinct methanogenic areas are present at the site: one zone is located directly beneath the water table; the second is located a few meters beneath the free phase oil. Both of the methanogenic reaction areas are separated by a reaction zone that is typified by iron reduction (Bekins et al., 2001). The iron reduction zone could explain why degassing at 534B (estimated by elemental ratios) is lower than qualitative gas exsolution estimates at wells slightly closer to the water table. Modeling efforts are carried out to confirm this hypothesis.  81  Figure 3.17. Methanogen MPN count per g of sample with depth, at three locations along the axis of the plume modified from information provided by Bekins et al. (2001). Methanogenic zones within the saturated zone are estimated and plotted along the cross section along the axis of the north plume.  3.5 Groundwater Flow Modeling  Flow modeling at the Bemidji site is conducted with Visual Modflow, so that particle path lengths can be evaluated. Modflow uses the finite difference approach; particle paths are determined with the Modpath package. The model domain is 2D. The x-axis extends 200 m outwards in both directions from the 0 point origin (well 421) along the horizontal component to flow, which corresponds to the axis of the plume. The z-axis ranges from the highest point along the water table, at an elevation of 424.1 m, to an impermeable till layer, located approximately 19 m beneath the water table. The grid spacing along the x-axis is 2 m in areas directly under the free phase oil and in the vicinity of all monitoring wells, and 10 m at all other locations. The spacing of the grid intervals along the z-axis range from 20 cm, at depths within 5 m of the water table, to 1 m, at all other elevations. The hydraulic conductivity at the site is 1 x 10-4 m s-1 in the primary sandy unit and 5 x 10-7 m s-1 in the silt layers. These values are within the range of estimated site hydraulic conductivities (Essaid et al., 1995). The porosity at the site is estimated at 0.38 and 0.30 in the sandy layer and silty layer, respectively. 82  The storage in all cases is assumed negligible. Recharge at the site is approximated as 0.2 m y-1 (Herkelrath and Delin, 2001) in elevated ground surface locations, and as 0.4 m y-1 at lower ground surface elevations. The average rate of groundwater flow at the site is approximately 3.0 x 10-7 m s-1 and is inputted into the model through two constant head boundaries positioned on the left and right side of the domain. The left boundary is fixed at 19 m (424.12 m) and the right boundary is held constant at 17.8 m (422.92 m). Modeling parameters are presented in Table 3.10.  Table 3.10. Aquifer properties and parameters and the associated literature values implemented in the saturated zone Modflow modeling of the Bemidji aquifer Modeling Parameter  Value  Source  Horizontal Conductivity - sand  1 x 10-4 m s-1  Essaid et al., 1995  Horizontal Conductivity - silt  5 x 10-7 m s-1  Amos et al., 2005  Porosity – sand  0.38  Essaid et al., 1995  Porosity – silt  0.30  Dillard et al., 1997  0.2 m y-1 / 0.4 m y-1  (Herkelrath and Delin, 2001)  5 x 10-7 m s-1  Amos et al., 2005  Recharge Specific Discharge (horizontal)  The top layer of the model is run under Type 1- unconfined conditions. Particle tracking is used to simulate water movement through the aquifer under steady state conditions. The particles are situated so that they will intersect the screen of the monitoring wells used for noble gas analysis. The particle path lines, methanogenic zones, silt layers, noble gas monitoring wells, and equipotential lines are presented in Figure 3.18.  83  Figure 3.18. Modflow domain as it applies to the Bemidji cross-section. Silt layers in the model are represented as lower conductivity layers. The lower till boundary is represented as an impermeable boundary. Methanogenic zones signify zones of high gas production. Equipotential lines and particle path lines are simulated under steady states conditions. The monitoring well and vapor well locations are illustrated along the axis of the north plume.  The path lengths are evaluated so that a conceptual model for the analysis of degassing and ebullition can be constrained. Particle path lengths for each well are presented in Table 3.11. The transport simulations suggest that groundwater passing through 315 has traveled approximately 60 cm before reaching the well screen, and mainly consists of recharge water. This recharge water only experiences methanogenic conditions. The passage of water collected at 534B is primarily through a zone that has previously been identified as dominated by iron reduction (Bekins et al., 2001), which provides reason for the relatively low degassing results. The groundwater sampled from 533B has passed through the lower methanogenic zone. The model results suggest that 532A water samples will consist of water that has traveled through the upper and lower methanogenic zones, so the highly degassed water sampled at 532A, is likely a result of gas stripping. Monitoring well 531A is screened in a primarily clean  84  upstream groundwater area; therefore, water passing through this will has not undergone significant degassing.  Table 3.11. Modflow monitoring well locations and screen depths and estimated particle path lengths, as calculated by Modflow and by velocity ratios Well  Top of Bottom of Screen Screen Elevation (m) Elevation (m)  Approx. Point of Water Extraction (m)  Estimated Path lengths (Modflow)  Path lengths Calculated by a Ratio of Horizontal/Vertical Velocity  310E  423.18  421.86  422.52  n/a  1.4/73.6  531A  423.70  422.17  422.94  10  1.2/40.3  532A  423.85  422.53  423.19  10  0.9/36.2  533B  420.30  420.14  420.22  110  3.9/193.3  533C  421.80  421.65  421.72  170  2.4/114.0  534B  422.92  422.77  422.84  50  1.3/50.4  315  424.68  423.16  423.43  0.70  0.6/19.5  3.6  Reactive Transport Ebullition-Inclusive Modeling  A simple reactive transport model is developed to evaluate how dissolved noble gas concentrations relate to degassing and ebullition at the Bemidji site. The groundwater sampled from monitoring well 315 exhibits the largest degree of gas stripping (Figure 3.7). All reactive transport modeling efforts focus on 315, so that the possibility of ebullition at the site can be either confirmed or refuted. According to the Modflow simulation, the approximate distance to the point of water extraction at the well is between 50 and 70 cm beneath the water table along the flow path. Modflow particle tracking suggest that it takes 100 days for water to reach a depth of 60 cm, and that flow is primarily downward. As outlined in Figure 3.2, processes that alter dissolved gas concentrations at well 315 include diffusion, advection, and gas-water partitioning. Dissolved gases in the system can also be replenished by diffusion and advection of the 85  flowing groundwater. The noble gas ratios show strong evidence of degassing; however, the occurrence of ebullition remains questionable.  The reactive transport model, used to evaluate ebullition, adopts the Lagrangian stream tube approach and applies it to a Eulerian framework. The Lagrangian method tracks a parcel of water through a system and is appropriate when advection is the driver behind gas transport. A Eulerian model will constrain transport to a stationary grid; water passes through a defined set of cells, but the compositional change over time or distance is related to the model domain and not the individual parcel of water. The stream tube approach monitors the water composition along the flow path, as predicted by the aforementioned Modflow simulations. Bubbles are stationary within the subsurface (save for ebullition events), and their gas composition can change with time; however, the dissolved gases are contained within a defined volume of water which itself is transported into the aquifer, requiring the implementation of a coupled modeling approach. The bubble and the diffusional processes associated with the model are constrained to the grid; however, the final dataset analyzed in the results is obtained by tracking the parcel of water as it passes through a defined set of cells.  3.6.1.1 Modeling Framework  The stream tube method tracks a 1 L packet of water through the subsurface. This approach sanctions the use of PhreeqC 2.121.669 (Parkhurst and Appelo, 2008). PhreeqC assesses the geochemical reactions, in the form of batch reactions, associated with 1 L solutions. The porosity of the aquifer in the silt layer is estimated as 0.3 (Table 3.10); therefore,1 L of dissolved pore water translates into a packet of bulk sediment with the dimensions 0.15 m x 0.15 m x 0.15 m, or an overall aquifer volume of 0.0033 m3. The groundwater will reach the well screen after passing through 4 pore volumes, 1 L each in size. Modflow particle tracking indicates that the flow is relatively constant along the flow path, and that water will remain in a 1 L pore volumes for 86  approximately 25 days. The transport keyword in PhreeqC was not used for the reason that it was unable to maintain entrapped gas partial pressures from cell to cell. Modeling parameters are summarized in Table 3.12.  Table 3.12. Modeling parameters associated with reactive transport ebullition modeling at monitoring well 315 Pore Vol #  Vol. of PhreeqC Batch Reaction (L)  Porosity Vol. of Vertical of Simulated Location of Aquifer Aquifer Pore Volume (m^3) with Depth from Water table (m)  1  1.0  0.3  0.33  2  1.0  0.3  3  1.0  4  1.0  Pressure in Centre of Pore Volume (atm)  Transport Time from Water Table (days)  0-15  0.9575  0  0.33  15-30  0.98  25  0.3  0.33  30-45  1.0175  50  0.3  0.33  45-60  1.07  100  In each pore volume, a certain proportion of said volume will be occupied by a gas phase. Determining when gas formed at the well is impossible, and little detailed information pertains to the rate of methanogenesis with time at the site. The total volume occupied by gas bubbles is predetermined for each batch reaction. The reactions are solubility controlled and, thus, the bubbles are assumed to be in equilibrium with the dissolved gas. The conceptual model is illustrated in Figure 3.19.  87  Figure 3.19. Conceptual model detailing the Lagrangian style reactive transport modeling of dissolved noble gases in the saturated zone of the highly methanogenic sediment at monitoring well 315.  88  3.6.2 Initial Conditions  Initial conditions are used as a starting point for the steady state evaluation of the groundwater composition at well 315. The initial conditions of the system are calculated as a function of the vadose zone under a solubility controlled regime. This approximation is implemented because the rate of methanogenesis, the rate of bubble growth, the vadose zone compositional change with time, and the rate of change of the gas saturation volumes are all unknown. The concentration of the dissolved gases in the water should be in equilibrium with the vadose zone. Additionally, the vadose zone gas composition will be dependent on the concentrations and amount of gas exsolving from solution as a result of ebullition. The acclimatization of the model towards steady state values is most accurately accomplished by equilibrating the top cell of the model with the vadose zone gas composition.  The groundwater contained within the first pore volume is in equilibrium with the vadose zone, and is stipulated by the gas measurements taken at well 9016 (Table 3.5). Dissolved gases are assumed to be in equilibrium with the observed partial pressures in the vadose zone, with a combined total pressure of 0.95 atm. For simplicity, a discontinuous gas phase is assumed to be present in the first pore volume, with an average pressure calculated at a depth of 7.5 cm beneath the water table. The hydrostatic pressure at this point will have increased the total pressure to approximately 0.9575 atm. The excess partial pressure in the bubble is attributed to CH4 and CO2 additions to the system at the point of gas exsolution. The amount of biogenic gas added to the system is the primary constraint used to calibrate the model.  The initial conditions are modeled using the “Solution” and the “Equilibrium Phases” keywords. The initial gas phase concentrations are representative of the overlying gas phase. The database of the system is user-defined for all reactions containing N2, O2, CO2, CH4, He, Ne, Ar, Kr, and Xe. The default database used to 89  simulate this system is the “llnl” database. The gas phase is simulated in PhreeqC by using the "Gas Phase" keyword. Gas exsolution occurs under a fixed pressure constraint, whereby the volume of the gas bubbles will fluctuate, but the pressure will remain constant. The initial volume of the entrapped gas phase is predetermined and is associated with commonly reported literature values (Amos and Mayer., 2006a). Gas saturation values in the model are considered at 5%, 10% and 20%. The "Reaction" keyword is used to add CH4 and CO2 to the batch system, in a 1:1 ratio. The dissolved gas concentrations are recalculated once the dissolved gases have equilibrated with the entrapped gas phase. The water and dissolved gases then pass into a successive pore volume.  The groundwater composition in the second pore volume is equal to the final solution of the initial pore volume. The initial composition of the bubble in pore volume 2 is in equilibrium with the final solution of pore volume 1. In all cases, the initial volume of the entrapped gas phase remains the same throughout the modeling domain, as does the amount of biogenic gas added to each pore volume. The modeling domain representative of monitoring well 315, has 4 pore volumes in total; the remaining two pore volumes are calculated in the same manner as above. The pressure constraint, under which gas exsolution occurs in each pore volume, changes with depth, and increases by 0.1 atm for every 1 m depth beneath the water table.  Diffusion is also taken into account and is constrained to the domain grid. The diffusion coefficients for each gas are presented in Table 3.8. The effective diffusion coefficients, implemented in the evaluation of the diffusive replenishment of noble gases to the pore water, are large. The diffusion length is taken from the vadose zone to the centre of the pore volume for all calculations. This approach likely overestimates the contribution of diffusion to the deeper cells. Water is assumed to remain within one pore volume for approximately 25 days. The addition of gas to each pore volume by way of diffusion is minimal during sample runs and does not significantly alter the results. The influx of gas at steady state will be offset by the ebullition flux, so long as 90  gas is replenished primarily by advection, which is the assumption with a steam tube approach to modeling.  3.6.2.1 Model Calibration  Each model is calibrated by matching Xe simulated concentrations to the actual Xe concentrations measured from water sampled at monitoring well 315. Varying amounts of biogenic gas are added during model runs. Simulations are generally characterized by a maximum saturation value. This value represents the amount of gas that can be held within the sediment and is set to 5%, 10%, and 20% of the batch volume. Ebullition will occur at saturation volumes greater than 20% (Amos, 2006). Model runs are evaluated based on a gas volume saturation level that is held constant throughout a simulation. Xe was initially selected as the calibration target because it is the gas that is least affected by diffusion and by air-water partitioning. This choice proved beneficial, because Xe was shown to attain a steady state concentration in advance of the other dissolved noble gases in solution. All results are normalized to 315 observed concentrations, which yields values expressed as fractions of the actual measurements, so that all results can be analyzed simultaneously.  3.6.3 Steady State Modeling of Degassing Ratios  A steady state assumption is applied to the model for the reason that the vadose zone gas composition has remained constant for a minimum of 6 years (Molins et al., 2009). If the saturated zone was not at pseudo-steady state, the amount of CH4 and CO2 entering the vadose zone would likely increase with time, given significant ebullition rates. The steady state approach is also implemented because the rate of bubble formation and gas storage with time is unknown. Additionally, the boundary conditions are approximated by a constant concentration along the top of the domain; however, 91  the evolution of this boundary has not been quantified and thus cannot be applied to a transient model. A transient model requires the input of too many unknowns into the system. A steady state approximation minimizes the variables, so that model calibration can be restricted to adjustments of the biogenic gas equimolar additions within each cell.  To attain a steady state, multiple volumes of water, containing dissolved gases, are flushed through the model domain. The steady state calculations follow the same methodology as the initial conditions; however, the composition of the entrapped gas phase is determined by the dissolved gas concentrations inherent to the previous simulation, in lieu of the upgradient pore volume. The exception to this is the initial run, where gas concentrations are a function of the vadose zone. With each successive time step, the change in dissolved concentration minimizes and the system approaches a steady state.  The number of time steps needed to calculate the steady state is set to the number of simulations required for dissolved Ar, Kr and Xe to reach constant values. It takes a much longer time for the lighter gases to attain a steady state concentration. The accuracy demanded of the lighter gases is generally less than the requirements imposed on the heavier gases, not only because the lighter gases tend to require a longer time to reach a steady state, but also for the reason that diffusion will alter these values more than it will the heavier gas values. Diffusion from the lower clean groundwater into the domain is neglected, and the diffusion entered into the model is merely an estimate. Deviations in values from steady state calculations would suggest that the system may still be under transient controls.  92  3.6.4 Steady State Modeling for Systems without Ebullition  The simulations that preclude ebullition as a possibility are calibrated to the maximum rate of biogenic gas production at the defined gas saturation, where gas saturation volumes will not increase. No accumulation of gas is needed for a steady state assumption to be valid; essentially, all of the CO2 and CH4 added to each cell is transported to the successive cell. The sediments are modeled at maximum gas saturations of 5% and 20%. The dissolved noble gas concentrations for degassing ratios calculated at steady state are presented in Table 3.13 and illustrated in Figure 3.20. The amount of gas added to the system results in a net zero growth for the entrapped gas phase. Simply put, the amount of biogenic gas roughly offsets the increase in hydrostatic pressure at the point of gas formation.  Table 3.13. Modeled dissolved noble gas concentrations normalized to actual 315 concentrations at steady state for degassing ratios not including ebullition events, and the associated biogenic gas additions and bubble volume increases, for specified gas saturation levels Gas Sat. Level  He / He(315)  Ne / Ne(315)  Ar / Ar(315)  Kr / Kr(315)  Xe / Xe(315)  Acc. Err  Biogen. Gas (mmols)  0.05  4.31  5.34  4.64  2.07  1.71  13.07  0.08  0.20  3.26  3.99  4.03  1.90  1.62  9.80  0.2  93  Figure 3.20. Dissolved noble gas concentrations, at well 315, as simulated by the degassing only model, normalized to actual dissolved concentrations of He, Ne, Ar, Kr, and Xe, for gas saturation values of 5% and 20% for steady state modeling without ebullition.  The results obtained from the steady state model without ebullition strongly suggest that degassing is not the only process altering gas concentrations at monitoring well 315. The error imposed on the heavier gases under a gas saturation rate of 20% ranges from 162% to 403% of the actual measured amount, for both Kr and Ar, respectively. The error in Ne can range as high as 530% of the actual value, for the 5 % saturation model. The system is either continually accumulating gas, or it is undergoing ebullition.  94  3.6.5 Transient Modeling for Systems without Ebullition  A transient simulation, without an ebullition component, is conducted to ensure that the ebullition results cannot be reproduced through degassing. For the transient simulation, the amount of biogenic gas is arbitrarily set to 0.5 mmols per cell, or a rate of 2.31 x 1010  mmol Lpore water-1 s-1. Past methane production rates in the saturated zone,  approximated from MPN data, is 2.40 x 10-9 mol Lpore water-1 s-1 (Bekins et al., 2005). The model is run under two distinct boundary conditions. One is set to the vadose zone gas composition found at background well 310 and the other is set to current day vadose zone conditions. The model is run for 200 days and concentrations are extrapolated to 1800 days. Boundaries set to background values yield the most inaccurate results; therefore, only current vadose conditions are presented for Ar, Kr and Xe in Figure 3.21. The dissolved noble gas concentrations do not fluctuate with time because the volume addition of gas is equal to the amount of biogenic gas added to the system. The observed values cannot be simulated for models that only consider gas exsolution. Furthermore, at the defined biogenic gas production rate the model will reach a gas saturation level of 20% within 800 days from the onset of methanogenesis. Methanogenesis has been ongoing at the site for much longer than 3 years. The transient model confirms that the steady state ebullition model is the most likely approximation of the mass flux out of the system as a result of ebullition.  95  Figure 3.21. Dissolved noble gas concentrations at well 315 as simulated by the transient model, normalized to the actual dissolved concentrations of Ar, Kr, and Xe, for an initial gas saturation values of 0%. The gas saturation values are allowed to increase with time and are represented on the lower x-axis. Ebullition is not considered in the system. The boundary conditions imposed on the transient model are those of current day vadose zone dissolved gas concentrations.  3.6.6 Steady State Ebullition Model  The steady state simulations, that consider ebullition, are conducted at gas saturation values of 5%, 10%, and 20%. The modeling results are conducted as described in the prelude to this section. The volumes are kept constant throughout the entire simulation. Excess gas produced during a pore volume calculation remains in the cell; however, the bubble volumes do not grow with successive pore volumes, or simulation runs. It is assumed that the excess volume exits the system via ebullition once the water leaves a cell. The exception occurs at the tail end of the modeling conducted at 5% gas saturation. The gas saturation value in this model grows in volume once it has reached 96  a steady state so that an evaluation can take place regarding the possible effect gas storage will have over the dissolved concentrations. The final results are summarized in Table 3.14 and in Figure 3.22. A typical input file is presented in Appendix E.  Table 3.14. Modeled dissolved noble gas concentrations normalized to actual 315 concentrations at steady state and the associated biogenic gas additions and bubble volume increases for specified gas saturation levels Gas Sat.  Ne / Ne(315)  Ar / Ar(315)  Kr / Kr(315)  Xe / Xe(315)  Biogen. Gas (mmol)  Ebullition* Vol. (L)  0.05  He / He(315 ) 0.21  0.25  1.00  0.84  1.04  1.28  0.1  0.10  0.26  0.29  1.00  0.84  1.04  1.28  0.1  0.20  0.38  0.43  1.02  0.83  1.03  1.28  0.1  0.05  0.19  0.21  0.99  0.85  1.04  1.28  0.155**  *The ebullition volume is a combined volume over all four cells in the model **no ebullition is considered in the model, the volume instead represents final gas saturation volume as a result of gas exsolution after 50 days.  97  Figure 3.22. Noble gas concentrations at well 315, as simulated by the ebullition model, normalized to actual dissolved concentrations of He, Ne, Ar, Kr, and Xe, for gas saturation values of 5% (A), 10% (B), and 20% (C) at steady state conditions Ebullition is removed from the model for the 5 % gas saturation model during the final 3 time steps, and degassing is allowed to ensue. 98  The simulated dissolved concentrations calculated with the ebullition model correspond relatively well to measured dissolved concentrations, and are much more constrained to actual concentrations than the values obtained with model runs based on a degassing-only premise. Modeled Ar concentrations initially appear uncharacteristically high, when compared against water sample results; the ebullition model is able to account for the much lower Ar readings, as measured in the field. Ar, Kr, and Xe all reach a relatively constant value, within 15% of the actual concentration, which is well within the confines of the error expected through the assumptions applied to the model, especially when coupled with the experimental error associated with the sampling and analysis procedures. He and Ne are associated with the largest deviations from sampled values at well 315. This discrepancy can be attributed to the long time intervals required for He and Ne values to attain a constant value. Additionally, background dissolved concentrations are depleted in He and Ne ratios and for this reason, the Ne and He values are omitted from analysis. It appears that larger gas saturation volumes yield Ne and He results that measure closer to sampled dissolved concentrations. These simulations remain relatively depleted in He and Ne, with respect to measured concentrations, in comparison to the other noble gases. Although this finding could suggest that the He and Ne values increase with larger gas saturation volumes, it most likely infers that the larger gas saturation volume simulations have yet to reach a true steady state or that gas accumulation in the sediment is ongoing. Another possibility is that an air bubble in the sample is falsely elevating lighter gas compositions.  The simulated gases, normalized to actual measurements and modeled using a 10% gas saturation volume, are plotted with depth in Figure 3.2. The figure suggests that depth also plays a role in the modeling accuracy. He and Ne simulated values could be overly stripped of gas as a result of slight inaccuracies in screen depth estimates.  99  Figure 3.23. Noble gases concentrations, at well 315, as simulation by the ebullition model at a gas saturation of 10%, normalized to vadose zone concentrations, plotted against depth for monitoring well 310. The biogenic gas production rate is 1.28 mmols per cell, or a rate of 5.78 x 10-10mols Lpore water-1s-1.  The amount of gas required to produce the observed dissolved noble gas concentrations is identical in all cases. Approximately 1.28 mmols of gas is produced in each cell per 25 days; the biogenic gas production rate is, therefore, 5.78 x 10-10 mols Lpore water-1s-1. The amount of methane produced is 2.89 x 10-10 mols Lpore water-1s-1, which is still well below the estimate provided by Bekins et al. (2005) of 2.40 x 10-9 mols Lpore -1 -1 water s .  Approximately 4 mL of gas is released to the vadose zone every day from 4 L  of pore water, regardless of the gas saturation value. The bulk area along the top of the domain is equal to 0.0225 m2. Therefore, the rate of gas release is approximately 0.177 L m-2 day-1. Numerical results are summarized in Table 3.15. The plume covers an area of approximately 80 m x 25 m. If the rate of release is extrapolated over the entire area, the total bulk release of gas is 354 L day-1. This amount of gas is significant and will impede the carbon mass balance calculation at the site. 100  Table 3.15. Overall findings pertaining to the steady state reactive transport ebullition modeling conducted at the Bemidji site at monitoring well 315 Rate of Biogenic Gas Ebullition Model Production Volume of Gas Area (mol Lporewarer-1 s-1) (mLgas/Lwater) (m2) 5.78 x 10-10  25  0.0225  Flux of Gas Across W.T. (L m-2 day-1) 0.177  Area of Total Amount LNAPL of Gas Loss (m2) (L day-1) 2000  354  3.6.7 Model Limitations  Limitations with the model include the exclusion of gas repartitioning from the bubbles into the pore water during bubble rise. The gas bubbles will rise, and the contents of the bubbles can be redistributed along the bubble migration path. This limitation is minimized so long as the entire depth is saturated with gas. Capillary forces must be overcome prior to a bubble forming in the subsurface. This process is overlooked with the reactive transport model. The migration path of the bubble out of the subsurface will be affected by heterogeneity and vadose zone total pressure fluctuations; however, these constraints are not imposed on the system. Furthermore, the LNAPL might trap bubbles under the water table, limiting the amount of gas that actually exits the system. Additionally, groundwater mixing and dispersion is not considered with the modeling efforts. Despite these possible limitations, modeling results correspond relatively well to actual concentrations.  3.7  Conclusion  The correlation between the dissolved background concentrations and vadose zone concentrations could suggest that excess air calculations are over estimated and that measured dissolved concentrations are actually a function of gas transport occurring within the vadose zone. Degassing can be characterized by depletions in noble gas dissolved concentrations, and can be related to the solubility controlled partitioning of 101  noble gases. The highest degassing rates are located within the source zone wells. Degassing is variable and is most likely affected by subsurface heterogeneity. The extent of degassing corresponds well to previous methanogen data provided by Bekins et al. (2005) and to Modflow simulation results. Ebullition in the source zone is sufficiently slow such that no evidence suggests kinetic fractionation, and thus, all ebullition in the source zone is solubility controlled.  Lagrangian style reactive transport modeling, with a PhreeqC geochemical interface, is implemented in the assessment of ebullition at the site. Modeling approaches that do not include ebullition, and simply simulate the observed gas concentrations under transient or steady state degassing-only specifications, are not able to reproduce actual dissolved noble gas concentrations. Moreover, modeled Ar concentrations, as determined through simulations that exclude ebullition, consistently and grossly overestimate observed Ar values. The ebullition model is able to accurately model measured dissolved Ar concentrations. The approximated average rate of biogenic gas production, as predicted by the ebullition model, is 5.78 x 10-10 mol Lpore -1 water  s-1. The rate of gas release, as predicted by the ebullition model, in the vicinity of  315, is approximately 0.177 L m-2 day-1. With the current modeling set-up for ebullition in an unconfined aquifer, the He and Ne values are the least accurate for two reasons. Dissolved He and Ne model concentrations require the largest number of calculations to reach steady state because they exhibit the largest deviation from initial conditions, which are a function of vadose zone gas compositions. Furthermore, any error in diffusion estimates will be the most pronounced in He and Ne measurements. Xe values require the least number of calculations to achieve a consistent simulated concentration and, therefore, biogenic gas initial estimates should be calibrated to Xe. In an unconfined aquifer, calibration parameters for ebullition modeling should focus on the heavier noble gases.  102  4  4.1  Laboratory Assessment of the Effectiveness of Nonreactive Gases as Tracers for Ebullition  Introduction  Laboratory experiments pertaining to ebullition are conducted under controlled conditions, as a supplement to current field data. The applicability of a point source gas tracer (SF6) and a constant source gas tracer (Ar) under closed conditions is examined in a column experiment. The results of the column experiment are later modeled so that rates of biogenic gas production can be approximated. The implications of Ar as a gas tracer of ebullition have previously been investigated by Amos and Mayer (2006a). A partitioning experiment further explores possible sinks for the point source tracer, SF6, and examines the influence of potential partitioning behavior over tracer suitability.  The concept behind the column experiment is that bubbles will form in a methanogenic organic matter zone (OMZ), located in the lower portion of the column. Methanogenesis will lead to an increase in the amount of dissolved CH4 and CO2 in solution. Bubbles form in the OMZ when the combined partial equilibrium pressure of all gases in solution is in excess of the total pressure at the point of bubble formation. Ebullition ensues so long as the anoxic degradation rates producing CO2 and CH4 are sufficient. As a result, bubbles migrate out of the OMZ, through a saturated clean sand layer, and, ultimately, enter a partially saturated column headspace. A similar column experiment was previously conducted by Amos and Mayer (2006a). Accurate monitoring of the column water level and the headspace pressure will enable an approximation of the extent of biogenic gas production in the OMZ. The process of ebullition can be confirmed through detection and analysis of the tracer gases Ar and SF6 in the column headspace. Both tracer gases are initially present in the OMZ. The use of nonreactive gas tracers is important for the evaluation of ebullition because both  103  CO2 and CH4 are reactive gases and can be consumed or produced in the subsurface and; therefore, may not accurately represent ebullition.  Ar is initially present in dissolved concentrations, in equilibrium with the atmosphere, throughout the column. Ar has been used previously to detect ebullition in lakes (Brennwald et al., 2005) and in deep groundwater basins (Zhou et al., 2005). SF6 is present at fixed concentrations in the OMZ of the column. SF6 has previously been used to detect subsurface flow in an aquifer (Harmon et al., 2003), it can act as a detector of DNAPL (Wilson and MacKay, 1995), and it was implemented in the evaluation of aquifer characteristics (Vulava et al., 2002). SF6 is selected as the point source tracer because it is not present in significant measurable amounts in the atmosphere; furthermore, it does not pose any adverse environmental consequences on a system and finally, it will partition readily into a gas bubble as it forms.  SF6 has a low diffusion coefficient (Vulava et al., 2002), therefore, diffusion of SF6 away from the source zone or out of the headspace will be minimal. SF6 is not very soluble in water. The repartitioning of the SF6 gas, contained in an upwards-migrating bubble, into the sediment free of SF6, will be minimal. However, because of solubility constraints, the dissolved tracer concentration will be low.  The solubility of SF6 in water is further complicated by the presence of contaminants. Methanogenesis is often associated with hydrocarbon contamination. SF6 is a polar substance and is more soluble in NAPL than in water. The presence of a separate NAPL phase is expected to deplete the tracer concentration, so long as it encounters the separate phase at some point during its migration. The extent to which hydrocarbons complicate the applicability of SF6 as a tracer is assessed with a partitioning experiment. The partitioning experiment, together with the column experiment, can be used to establish criteria for determining tracer suitability for future ebullition studies. 104  4.2  Part 1: Partitioning Experiment  A partitioning experiment is conducted to assess the applicability of SF6 in a hydrocarbon contaminated setting. The affinity of SF6 for hydrocarbons is assessed through a series of batch reactions that investigate the relationship between air and oil partitioning. The methodology implemented through Part 1 of this Chapter is based on methods and approaches detailed in Harner and Mackay (1995).  4.2.1 Sample Preparation  The ambient pressure is determined with a Fisher Scientific Standard Atmospheric Barometer. The temperature is measured with an OMEGA digital K-rated thermometer. Changes in the ambient conditions throughout the duration of the experiment were negligible. SF6 oil partitioning samples are prepared in 10 mL Kimble Autosampler headspace vials. Motor oil is added to the vials with a 5.0 mL volumetric pipette. The vials are capped with butyl headspace vial caps and crimped immediately following the hydrocarbon additions. Specified volumes of SF6 are added to the air filled headspace. Additional volumes of air are added to the headspace using a 3 mL and a 0.5 mL Pressure-Lok  ®  Hamilton syringe. The SF6 volumes are prepared by expanding SF6  directly from the Praxair cylinder into an evacuated 1 L calibration column, fitted with an Ashcroft Low-Pressure diaphragm gauge and an attached butyl septum. The pressure in the calibration column is adjusted to atmospheric pressure. The volumes of SF6 are extracted from the calibration column through the septum using a Hamilton PressureLok ® syringe. The extraction volumes are sufficiently small so that the change in column pressure is unaffected by SF6 volume extractions. Sample details along with SF6 and air volumes are summarized in Table 4.1.  105  Table 4.1. Summary table of partitioning experiment SF6 sample details Sample  Initial Air Volume (mL) at 101.125 kPa/20°C  Added SF6 Volume (mL) at 101.125 kPa/20°C  Added Air Calculated SF6 Initial Atm. + Volume (mL) Gauge % at 101.125 Pressure kPa/20°C (kPa)  1  5.0  0.00  3.00  0.0  129  2  5.0  0.02  2.98  0.25  128  3  5.0  0.08  2.92  1.0  130  4  5.0  0.10  2.90  1.3  128  Immediately following sample vial air additions, the pressure in the vials is measured using a USG 30 psi pressure gauge secured through NPT connections to a gas tight needle. The gauge pressure readings are variable (Table 4.1); however, this variation is negligible and is attributed to the premature partitioning of sample gas as a result of sample disturbance or due to gas leakage during volume additions. The samples are shaken vigorously for 20 minutes and allowed to sit for 2 hours prior to analysis.  Calibration samples are prepared in Kimble Autosampler headspace vials. The standards are prepared in the same manner as above, but without the addition of oil to the vials. The initial amount of SF6 in the sample is measured as a percentage of the total gas volume, as are the calibration standards. The calibration volumes and associated pressures are presented in Table 4.2.  106  Table 4.2. Calibration standard preparations volumes implemented in the analysis of the SF6 oil-gas partitioning experiment associated with the OmniStar Gas Analyzer readings Calibration #  Initial Air Added SF6 Added Air Calculated SF6 Atmospheric Volume (mL) Volume (mL) Volume (mL) % + Gauge Pressure at 101.125 at 101.125 at 101.125 KPa/20°C KPa/20°C KPa/20°C (kPa)  1  10.0  0.00  5.00  0  125  2  10.0  0.01  4.99  0.0666  127  3  10.0  0.05  4.95  0.332  130  4  10.0  0.10  4.90  0.662  129  4.2.2 Gas Analysis  The SF6 percent composition of the sample vial headspace is measured with an OmniStar Gas Analysis System GSD 301. The inlet capillary attached to the OmniStar Gas Analyzer is fitted with a 1/16th” swagelok assembly, which is attached to an NPT adapter fixed to a gas tight needle. A butyl septum is secured to the end of the needle in between calibration and sample readings to prevent air contamination of the gas inlet system. The SF6 ion counts are measured with the SEM detector on mass 127. The PKR gauge is enabled during sample analysis. The MID file utilized is “oil partitioning”. The pumping intake of the OmniStar Gas Analyzer is dependent on the sample pressure and temperature.  4.2.3 Results of Partitioning Experiment  Sample total pressure values are recorded prior to sample analysis to account for pressure fluctuations as a result of oil vapor additions to the gas phase and partitioning of headspace gases into the oil. The maximum ion counts of all samples and standards are normalized by the final sample pressure reading. Normalizing the samples to pressures is possible because pressure discrepancies between samples at time 0 107  assume identical volumes. Sample mole fractions are calculated based on linear regression techniques applied to calibration standards. The sample mole fractions are presented in Table 4.3.  Table 4.3. SF6 mole fractions in the headspace of oil-gas partitioning experiment samples, upon equilibration with the oil phase, as measured by OmniStar Gas Analyzer Sample #  Final Atmospheric + Gauge Pressure (kPa)  Ion Count (A)/Final Gauge Pressure (kPa)  SF6 %  1  115  6.99x10-13  0  2  115  8.01x10-10  0.0557  3  120  4.11x10-9  0.296  4  115  5.36x10-9  0.3861  4.2.4 Discussion of Partition Experiment  The oil-air partitioning coefficient KO−G represents the dimensionless ratio between the SF6 concentration in the vapor phase ( CG ) and the concentration in the dissolved phase ( CO ). As long as the volumes between the two phases are equal, the coefficient can be approximated by (Harner and Mackay, 1995): KO−G =  CO nO = CG nG  [22]  The initial number of moles in the sample headspace is approximated as the total number of moles injected. The percentage of SF6 in the vapor phase is calculated by assuming that the volumegas/volumetotal is representative of the mole fraction determined through analysis with the OmniStar Gas Analyzer. The repulsion and attraction forces between molecules are neglected during analysis.  108  The initial total number of moles in the headspace ( nT ) and the final number of moles in the headspace ( nG ) is approximated using the ideal gas law, where the volume is 5 mL and the temperature is 293.15 K. The number of dissolved moles in the oil ( nO ) can be approximated by equation [23], calculations are summarized in Table 4.4. . nT = nG + nO  [23]  Table 4.4. Total moles of SF6 in the gas and oil phase, at equilibrium, for samples analyzed in the oil-gas partitioning experiment Sample  Moles in Air  Moles in Oil  1  0.00000  0.00000  2  0.00013  0.00053  3  0.00073  0.00194  4  0.00091  0.00253  The moles of SF6 in the oil are plotted as a function of moles held in the gas phase; the resulting slope is the partitioning coefficient. The volume of gas in the headspace is identical to the volume of the oil; therefore, the volume term can be eliminated from the equation. The dimensionless partitioning coefficient is approximately 0.73.  109  Figure 4.1. For samples in the oil-gas partitioning experiment, the total moles of SF6 contained within the oil, plotted against the total moles of SF6 in the headspace, at equilibrium.  An estimate of the SF6 partitioning coefficient between water and oil is calculated. Henry’s constant for SF6 at STP is 2.75 x 10-4 mol L-1 atm-1 (Sander, 1999). Multiplying this value by the gas constant and the temperature in Kelvin approximates the dimensionless form of Henry’s constant. The partitioning coefficient of SF6 between the concentration in the water ( CW ) and the overlying gas phase, ( K G −W ), is approximately 149, where; KG−W =  CG = k Hx CW  [24]  K O −W , the partitioning coefficient between SF6, dissolved in the water and the dissolved oil ( CO ), can be approximated by:  110  KO−W =  CO = KO−G KG−W = 109 CW  [25]  As calculated, the K O −W of SF6 is approximately 109. All calculated partitioning coefficients are summarized in Table 4.5. Although, essentially all of the SF6 will partition into a bubble, these results suggest that SF6 also has a high affinity for oil. The amount of SF6 leaving the gas phase and entering the vadose zone will strongly depend on the interactions with free phase oil in the system and on the rate of ebullition. A table detailing the feasibility of SF6 as a gas tracer, under different ebullition fluxes, with varying amounts of encountered hydrocarbons, is provided in Appendix F.  Table 4.5. Dimensionless partitioning coefficients of SF6 for oil-gas partitioning, air-water partitioning, and oil-water partitioning KO-G KA-W KO-W 0.73  4.3  149  109  Part 2: Column Experiment  4.3.1 Column Construction  An SF6 tracer experiment is conducted under controlled conditions in a 2 cm thick airtight plexiglass column (Figure 4.2). The column is equipped with a pressure release system, a mass spectrometer, a low-pressure diaphragm gauge, and an inlet valve located at the base of the column. The upper flange of the column is connected to a mass spectrometer for headspace analysis. The inner column height reaches 61 cm and has an 8.22 cm diameter. The column is also fitted with an upper and lower flange assembly. The inlet port consists of a ball valve secured to the lower flange, attached to the columns via 1/4” NPT fittings. The upper flange in the column is equipped with a Swagelok low-flow metering valve and ball valve system connected via NPT and Swagelok fittings. This configuration enables the release of excess pressure from the 111  system. A 1/8th inch Swagelok tube connects the column directly to the Omnistar Gas analyzer. At the base of the tube, a Swagelok ball valve separates the column from the Omnistar Gas Analyzer. Additionally, an Ashcroft low-pressure diaphragm pressure gauge is attached to the flange. Ambient pressure readings are measured with a Fisher Standard Atmospheric Barometer.  Figure 4.2. Ebullition column details, with the column constructed out of 2 cm Plexiglas. The base of the column contains a ball valve used for tracer injections. A second ball valve is located midway up the column. A pressure relief port is located at the top of the column. The column is fitted with an Ashcroft low pressure gauge and an additional port, which is attached to an OmniStar Gas Analyzer. The column consists of a sediment phase, water phase and a gas phase. The sediment phase consists of an organic matter zone, a gravel zone, and a 30 mesh Ottawa sand zone.  112  4.3.2 Composition of Column Fill  The column fill consists of a lower organic layer, a thin gravel layer, and a thick sand layer. Organic matter in the organic matter layer (OMZ) is obtained from a drainage ditch in Richmond, BC. The organic matter is mixed with 20 mesh Ottawa sand in a 40:60 by volume ratio. The volume of the organic layer is approximately 877 mL. The porosity of the organic layer is estimated at 0.3. The volume of the gravel layer in the column is 106 mL, with an estimated porosity of 0.45. The volume of the sand layer in the column is 1344 mL. The total volume of the column occupied by sediments is 2.327 L. A complete list of the volumes and porosities associated with each layer is provided in Table 4.6.  Table 4.6. Column construction details for the column ebullition experiment OM Layer  Gravel Layer  Sand Layer  Bulk Layer  H2O Layer  Height of column  16.5  2.0  25.0  43.5  4*  Volume of Layer  876  106  1344  2327  200*  Porosity  0.3  0.45  0.36  n/a  1  Volume of void  262.8  47.7  483.84  794.34  0*  * Value will fluctuate as column experiment progresses  Initially, 200 mL of distilled water equilibrated with atmospheric gases (WEA) is added to the column. A saturated organic matter and sand mixture is added to the WEA and mixed thoroughly. During column construction, the sediments are added under saturated conditions and continually mixed to avoid entrapment of air bubbles. A gravel matrix is placed atop of the organic matter. The remaining WEA is suctioned out of the column to a level just above the gravel layer. This water is replaced with clean WEA, and the process is repeated, until the headspace water is clean. The gravel layer is overlain by 20 mesh Ottawa Sand. WEA is added overtop of the gravel layer. Sand is placed in the WEA to a level slightly below the water table. The sand layer is thoroughly mixed after each successive sand addition; the sand is always added to the 113  column under fully saturated conditions. Two centimeters of water are left atop the sand layer. The column is flushed with WEA, with flow traveling from the headspace layer to the base of the column. After column completion, the column is closely inspected for the presence of bubbles. None were detected.  4.3.3 Tracer Test Method  The column is left open to the atmosphere for 11 days, at which time the column is sealed. Twenty-two days after initial construction of the column, an SF6 tracer solution is injected into the OMZ at the base of the column. The tracer solution is prepared by bubbling SF6 through 1 L of distilled water for 1 hour. The SF6 is bubbled directly from the gas cylinder through the water contained in a 2 L drum, fitted with a pressure release hole so that the excess gas can escape. The tracer solution is pumped, with a peristaltic pump through gas impermeable Viton™ tubing, into the column. Prior to pumping, excess water from the column is drained slightly so that the column valve is saturated with water. The tracer-containing water is pumped through the entire length of the tubing for 2 purge volumes before it is attached to the inlet valve. The total volume of injected tracer solution is 130 mL of water. The head in the system rises by 0.5 cm. The ambient pressure and temperature are monitored throughout the duration of the column study.  4.3.4 OmniStar Gas Analyzer Method  The gas from the column headspace is pumped directly into the OmniStar Gas Analyzer. The column gas composition is determined by applying linear regression to calibration gas standard measurements. Praxair's Primary Laboratory Gas Mixture standards are pumped into the OmniStar Gas Analyzer from a 0.5 L calibration column with a volume adapted to the column headspace volume. The SF6 standards are not purchased in bulk at different vol/vol mix ratios. Specific volumes of SF6, extracted at atmospheric pressure, are injected into the fixed volume calibration column, at known 114  temperatures. The calibration gases are mixed on a vol/vol basis. The assumption is that a vol/vol ratio accurately represents a mole fraction, as the pressure and temperature of the calibration column is constant throughout an analysis period. For this assumption to hold true, all gases in the system should behave as ideal gases  The OmniStar Gas Analyzer measures ion counts in units of amperage. Each calibration gas contains a different per volume percentage of various gas components. The pressure, volume and temperature of the system are controlled to ensure that the total number of molecules of each gas remains the same throughout the experiment, as demonstrated through the ideal gas law. This constraint in system parameters allows for the calibration of different gases on a per mole (or per volume) basis.  The R2 term of each individual calibration line for every gas component is greater than 0.95. As a result of CO2 cracking, the N2 measurements are erroneous. All gases are measured using the Faraday cup, with the exception of Ar and SF6, which are measured using the SEM detector. A peak jump method file is used to determine gas concentrations at defined mass numbers. The mass on which each component gas is read, are detailed in Table 4.7.  Table 4.7. Omnistar Gas Analyzer – Column method setup details Gas  Mass  Detector  Calibration Points (%)  N2  28, 29  Faraday  78, 80, 98  Ar  40  SEM  0.2, 0.934, 2  CO2  44/45  Faraday  0.001, 1, 3  CH4  15  Faraday  3, 5  SF6  127, 108  SEM  0.01, 0.1, 1  O2  32  Faraday  0, 20.9  115  4.3.5 Results of Column Experiment  4.3.5.1 Physical Measurements  The water level of the column is measured with every temperature and column pressure measurement. The water level initially increases rapidly, but soon reaches a constant volume. Daily measurements are recorded in Appendix G. The increase in the headspace pressure, as a result of biogenic gas production is converted to a volume, measured in cubic centimeters (cm3) and normalized to the initial temperature and pressure (Table 4.8), recorded during the first column reading.  Table 4.8. Initial column physical measurements for the ebullition column experiment Ideal Gas Law Variable  Value  Pressure (kPa)  101.6  Temperature (20°C)  20.7  Total Moles (mol)  0.02563  Volume of gas* (cm3)  616.34  *The volume used to calculate the moles of gas in the system is calculated as a function of pressure range and is subject to change  The number of moles in the headspace at initial conditions, prior to any increases in pressure, is determined by using the ideal gas law. The change in pressure, and volume and temperature, at time i are taken into account when calculating the number of moles of each gas in the system. Although the actual headspace volume is fixed, calculations are carried out to account for the theoretical volume changes throughout the system, enabling the assessment of the volume of gas released. The change in volume is calculated by substituting the number of moles, at time i, into the ideal gas law, with all other variables set to initial conditions. The change in volume at time i is added to the initial volume to determine the amount of gas in the headspace at time i. The cumulative volume is also calculated in this manner. Additionally, the change in 116  volume of the system is verified using Dalton’s Law of partial pressures. The volume of gas released ( VR ) to the atmosphere is calculated by the equations: PoVo = PiVi  [26]  VR = Vi − Vo  [27]  The cumulative volume increase (measured as column pressure increases) and the volume change in water level with time are presented in Figure 4.3.  Figure 4.3. Water level change and accumulative volume of gas released from the columns as a result of biogenic gas production.  The total rise in the water level of the column is 3.5 cm, which translates to a volume of roughly 185 mL. The water levels measured in the column appears to decrease around the 90 day mark. This probably represents a daily measurement error, as a leak would most likely be indicated by a continual decline in water level. The water table reaches a constant value within 34 days. The most significant water table rise occurs within the first 10 days; during this time period, no gas is trapped in the 117  headspace. It is assumed that a majority of the produced gas is trapped within the sediment pore space. The total volume of gas released from the column and trapped in the headspace over the 119 days that the column was analyzed is 1280 mL. The increase in biogenic gas production for the first 60 days of the experiment appears linear. The rate at which gas contributes mass to the headspace as a result of methanogenesis and ebullition is approximately 10.75 mL day-1, which yields an ebullition flux of 1.91 L m-2 day-1.  Initially, the water in the column is equilibrated with atmospheric gases. The atmospheric partial pressures are presented in Table 4.9. During the first 11 days of the column experiment, biodegradation and phase transfer processes occur under open system conditions. After 11 days, the column is isolated from the ambient conditions and behaves as a closed isochoric system. The system itself is not entirely closed, as controlled and well-defined volumes of gases are allowed to exit the column at specific instances. Table 4.9, also summarizes the initial composition of gases in the headspace of the closed column. N2 is not included in the data analysis for the reason that CO2 and CH4 cracking impede accurate readings. The change in the mole fractions of the reactive gases in the headspace, specifically CH4, CO2 and O2, are illustrated in Figure 4.4; the headspace mole fractions of the nonreactive gases SF6 and Ar are presented in Figure 4.5.  Table 4.9. Initial headspace conditions of the column experiment Gas  Initial Conditions vol/vol %  N2  78.08  Ar  0.934  CO2  0.03  CH4  0  SF6  0  O2  20.9  118  Figure 4.4. Column headspace reactive gas % composition determined with an OmniStar Gas Analyzer.  Figure 4.5. Column headspace nonreactive gas % composition determined with an OmniStar Gas Analyzer.  119  The mole fractions illustrated above, represent the headspace gas evolution in a closed system (over the measurement interval); they neglect changes to mole fractions as a result of temperature and total pressure fluctuations. Initial gas mole fractions of Ar, N2, and O2 might mask gas signals representative of ebullition. The gas mole fractions are evaluated further in the discussion portion of this chapter.  4.3.5.2 Methane  The amount of CH4 entering the headspace at early time rapidly increases. After approximately 22 days (11 days after column closure) CH4 reaches a steady state of 24 %. The point at which CH4 reaches a steady state corresponds roughly to when headspace O2 becomes completely depleted.  4.3.5.3 Oxygen  The O2 in the headspace is consumed rapidly. During the initial 17 days of the experiment, the O2 declines at an approximate rate of 0.35 % per day. After 17 days, the rate at which O2 is consumed increases. The headspace is completely depleted of any O2 by day 22.  4.3.5.4 Carbon Dioxide  The CO2 headspace mole fractions are extremely variable. They appear to increase quite substantially during early time but become depleted post the 60 day mark. CO2 can participate in an array of biogeochemical reactions. CO2 was subject to the largest error as a result of its complex geochemistry but also because of calibration gas limitations and methodology errors. CO2 analysis is largely ignored for the remainder of this chapter. 120  4.3.5.5 Argon  Ar in the closed column headspace is 0.934% of the total pressure at initial conditions. Ar values peak on day 22, which initially seems counterintuitive to what is expected, as CH4 and CO2 molar additions to the headspace should promote a decline in the Ar mole fraction. A possible explanation is that Ar stored in the dissolved pore water is entering the headspace as a result of ebullition, or that O2 consumption as a result of CH4 oxidation is promoting an increase in the Ar reading. After day 22, headspace Ar rapidly depletes. An additional Ar peak appears on day 50. The Ar peaks correspond to peaks in CO2 and to the rapid increase in CH4 entering the headspace.  4.3.5.6 SF6  SF6 first appears in the headspace on day 24, two days post SF6 injection. The highest SF6 mole fractions in the headspace are detected on day 49, which is 27 days after initial injection. This suggests that the column was largely stripped of SF6 within 27 days, which infers that attenuation may occur as bubbles migrate upwards through the column. The amount of headspace SF6 is highly variable from day to day. This may be a function of the distribution of SF6 through the column. SF6 fractions appear to decline near the end of the experiment.  4.3.6 Biogenic Gas Production in the Column  The initial rise in the water level can be attributed to gas accumulation in the organic matter zone, and to a lesser extent, the overlaying sand layer, prior to significant ebullition events. A previous ebullition study by Amos and Mayer (2006a) observed that gas remains trapped in an organic matter layer until 29% of the pore space (11% bulk content) is saturated with gas, with only small amounts of gas able to escape prior to 121  aqueous gas saturation levels being reached. An additional study by Baird et al. (2004) determined that the bulk volumetric gas content of a peat during ebullition will range from 0.05 to 0.15 and that the process of ebullition is variable.  The total water level rise in the column is 3.5 cm, which translates to a total volume change of 185 mL. The volumetric gas content of the column is within the range recorded by Baird et al. (2004). It appears that a large proportion of bubbles are held in the organic matter zone and within the column itself. This is confirmed by visual observations.  A change in the column water level alters the headspace pressure by compressing the gas. The vast majority of the water level rise occurs while the column is open; any changes to the headspace pressure during this time are ignored. Post column closure, the water level continues to rise another 0.3 cm, or an additional volume of 15 mL. A volume change in the headspace of this magnitude, according to the Law of Partial Pressures, results in a pressure increase of approximately 0.02 atm. The actual rise in pressure over this range is 0.15 atm. This suggests that ebullition contributes significantly to the flux of gas through the system at early times. Moreover, even though it is unknown if methanogenesis is the main contributor to the initial gas volumes, it is probable that carbon mass loss in the system occurred.  4.3.7 PhreeqC Gas Simulation of Column Experiment  Gas production in the OMZ is simulated using the USGS low temperature aqueous geochemical modeling program, PhreeqC 2.121.669 (Parkhurst and Appelo, 2008). PhreeqC calculates the partitioning of gases between the dissolved phase and the gas phase of a bubble, which forms under a constant pressure. The simulated bubble represents the entrapped gas phase held within the OMZ sediment pore space. The headspace gas of the column is not modeled for the reason that the headspace gas is 122  not in equilibrium with the dissolved pore water in the OMZ; the partial pressures in the gas phase, as calculated by PhreeqC, are based on the assumption that gases are in equilibrium with the water.  The volume of produced gas in the column headspace is used to calibrate the model. Bubble growth in the OMZ is a function of the rate of formation of CH4 and CO2. Molar biogenic gas additions are incorporated into the simulation. The volume of the simulated gas phase formed in the OMZ is a function of the rate of excess gas entering the experimental column headspace, as a result of ebullition. The entrapped gas in the OMZ is periodically eliminated from the PhreeqC modeling domain, in an attempt to approximate ebullition. The initial accumulation of gas in the column occurs primarily under unconfined conditions (prior to column closure). This volume of gas stored in the column is taken into account with the PhreeqC simulation. The PhreeqC conceptual model is illustrated in Figure 4.6. The preliminary assumptions implemented in the conceptual model of the PhreeqC simulation are outline below.  123  Figure 4.6. Conceptual model detailing gas transport in the PhreeqC simulation of the OMZ of the column.  The model simplifies the 1D-column experiment to a batch system. The ebullition in the column is modeled by removing the entrapped gas phase from each successive batch reaction. This will overestimate the amount of gas that is leaving the column during each ebullition event but is used as a baseline for gas analysis. The PhreeqC simulation describes a closed environment; however, the column is left open for the first 11 days following column construction. Gas replenishment in the OMZ, as a result of inward diffusion, is assumed negligible; thus enabling the close system assumption. Bromide measurements, taken by Amos and Mayer (2006a), determined that diffusion was negligible in a similar a column experiment. Furthermore, Fick’s Law calculations, provided in Appendix H, strongly indicate that diffusion of gas into the OMZ will be minimal.  124  In order for gas exsolution to occur, the sum of the partial equilibrium pressures of all dissolved gases must be greater than the total pressure at the point of gas production. The average pressure of the headspace is 1.03 atm (104.35 kPa), and the point of gas exsolution occurs on average 42 cm beneath the water table in the OMZ. The fixed pressure under which bubble formation occurs is therefore, on average, 1.07 atm. The maximum entrapped gas volume is set to 32 % of the total pore space. This is considered a reasonable estimate as it was close to the value obtained for reactive transport modeling of an identical column, conducted by Amos and Mayer (2006a), with identical sediment compositions. Input file parameters are provided in Table 4.10.  Table 4.10. Input parameters for the PhreeqC modeling of the ebullition column experiment Model Variable pH  Closed System Simulation 7  Bubble Formation Pressure  1.07 atm  Temperature  20°C  Model database  LLNL  Components User Defined Approximate volume of each bubble  N2, SF6 85 cc  N2  0.708 atm  Ar  0.0934 atm  SF6  3.6 x 10-5 mol (per pore volume of OMZ)  The llnl database is used for all PhreeqC model runs. SF6 is not included in the database and is added manually (Table 4.11). Furthermore, unwanted reactions alter simulated N2 dissolved concentrations. To rectify this problem, N2 is user defined.  125  Table 4.11. Supplements to the PhreeqC data base implemented into OMZ input file Component  Henry’s Constant Source  SF6  2.75 x 10-4 [mol L-1] atm-1 (Sander, 1999)  O2 is omitted from the PhreeqC simulation. Column readings, obtained during the column experiment, infer that the consumption of O2 in the headspace is rapid. Additionally, CH4 is detected in the headspace, immediately after column closure, which suggests that the onset of ebullition, as a result of CH4 production, occurs prior to column closure. Methanogenesis will not ensue if O2 is present in the system; therefore, O2 measurements are excluded from PhreeqC modeling. This simplified approach is adopted for the reason that the focus is primarily on the tracer gas behavior.  On day 20, 130 mL of SF6 tracer water is injected into the pore water of the column of the organic layer. The assumption that the tracer water is saturated with SF6 is applied to the mass balance calculations, as an upper bounds. The maximum possible concentration of dissolved SF6 at a partial pressure of 1 atm is 2.75 x 10-4 mol L-1. Therefore, in total, 3.6 x 10-5 moles of SF6 are added to the OMZ. For modeling ease, it is assumed that the SF6 expanded into the total volume of pore water in the OMZ. This assumption is likely not valid, and thus can be used to explain variability in the dataset.  4.3.7.1 PhreeqC Modeling Results  The PhreeqC modeling results are presented in Appendix H. The CH4 mole fractions in the gas phase are initially much higher than CO2 as a result of the relatively high solubility of CO2. This is illustrated in Figure 4.7. Early conditions suggest that carbonate speciation reduces the amount of CO2 available for gas-water partitioning. 126  As the system becomes progressively enriched in biogenic gases, the pH of the system will decline, and the carbonate speciation will be dominated by carbonic acid. At later time, the system will become completely saturated with respect to both CH4 and CO2; the mole fraction of the biogenic gas held in the entrapped gas will essentially be equal for both CO2 and CH4.  Figure 4.7. Moles of CH4 and CO2 in the entrapped gas phase of the OMZ, which is subject to ebullition and thus occupies a relatively constant volume, in a close column environment plotted as a function of the volume of biogenic gas produced.  In a closed system, at the simulated rate of gas formation, all nonreactive dissolved gases in the OMZ become rapidly depleted. Initially, the dissolved gas concentrations of N2 and SF6 exceed that of Ar. Subsequent to 6 simulated ebullition events, the dissolved Ar becomes the largest nonreactive gas component in solution, albeit at extremely low values. SF6 shows the steepest rate of decline, which corresponds to its high affinity for the gas phase. The negative correlation between the  127  volume of gas produced and the nonreactive gas mole fractions, in the OMZ, is presented in Figure 4.8.  Figure 4.8. Moles of nonreactive gas in entrapped gas phase in the OMZ, which is subject to ebullition and thus occupies a relatively constant volume, in a closed system environment, plotted as a function of the volume of biogenic gas produced.  4.3.7.1.1 PhreeqC Results as they Pertain to Noble Gases  Noble gases are added to the PhreeqC input file for comparison purposes only. The results are plotted in Figure 4.9. Modeling results indicate that noble gas depletion in the pore water can be related to each noble gas by their mass. He and Ne dissolved concentrations decline, as a result of ebullition, much quicker than Kr and Xe in solution. The dissolved concentration of all of the noble gases decreases to near nondetectable levels for the reason that in a closed system the gases are not replenished through advection or diffusion following ebullition events.  128  Figure 4.9. Molality of noble gases dissolved in the pore water of the OMZ, where the entrapped gas phase is subject to ebullition, and thus occupies a relatively constant volume, in a closed system environment, plotted as a function of the volume of biogenic gas produced.  A PhreeqC simulation of the OMZ under non-ebullition conditions is also conducted. The bubble is allowed to grow indefinitely and does not exit the system. The noble gas molalities obtained from the degassing simulation are illustrated in Figure 4.10.  129  Figure 4.10. Molality of noble gases dissolved in the pore water of the OMZ, where the entrapped gas phase is not subject to ebullition, in a closed system environment, plotted as a function of the volume of biogenic gas produced.  The dissolved gas concentrations in the degassing simulation differ from the ebullition simulation in that Ar dissolved is solution will never approach Xe values, even at unrealistic volumes of produced gas. For Ar values to approach Xe values, ebullition must ensue. In the degassing model, the entrapped gas is always allowed to repartition back into the dissolved phase. The comparison of the Ar concentration to the heavier noble gases (mainly Xe concentrations) is a key analysis parameter. An identical trend is noted with the ebullition model in Chapter 3. The Ne and He concentrations quickly approach dissolved Xe concentrations, as a result of their similar initial concentrations. The extent to which the Ar/Xe ratios differ between the ebullition simulation and the degassing simulation in the OMZ is plotted against the volume of gas produced, in Figure 4.11.  130  Figure 4.11. Ar/Xe dissolved noble gas ratio in the OMZ of a closed system environment, plotted as a function of the volume of biogenic gas produced, for systems including and excluding ebullition.  Prior to the first ebullition event, indicated on the figure as the first visible black dot, the Ar/Xe ratios calculated by the ebullition model are identical to those computed with the degassing model. The model results indicate that when a bubble exits the system, and a new bubble forms, a larger proportion of the lighter gases will be removed from the OMZ. This process is exaggerated with the current modeling setup, but the concept still applies to sediments undergoing ebullition. Once the Ar repartitions into a newly formed bubble, the Ar/Xe ratio will decline even further, as the water becomes progressively depleted in the lighter gases, relative to the heavier gases. Although noble gas volumes are not measured directly during the column experiment, with the exception of Ar gas, modeling of the closed system behavior can provide a baseline for future experiments.  131  4.3.8 Discussion of Column Experiment  The following section pertains to the gas collected in the column headspace and imparts these findings to the PhreeqC OMZ modeling results, when applicable. The noble gas values, with the exception of Ar, are omitted from the discussion portion of this Chapter, as they were not detected in the headspace during column analysis. The CO2, and N2 readings are also largely omitted from analysis as a result of their associated large measurement errors due to method applicability and calibration standards.  4.3.8.1 Methane  The amount of CH4 contained within the headspace increases rapidly upon column closure. This suggests that methanogenic conditions are attained early within the experiment timeframe. The headspace mole fraction of CH4 does not appear to deviate from 24%. The moles of CH4 entering the headspace are calculated through manipulations of the ideal gas law. The calculations pertaining to the amount of moles of each component gas within the headspace are detailed in Appendix I. The calculations account for the moles of gas leaving the system by way of pressure release events. The total molar increase of CH4 entering the headspace appears to be quite linear when compared against the volume of gas produced, suggesting that the composition of the gas bubbles entering the headspace is constant (Figure 4.12); however, the rate at which CH4 is produced and enters the headspace is not linear (Figure 4.13). The nonlinear relationship could suggest that gas storage in the column increases with time, which consequently reduces the rate that CH4 enters the headspace per day. Tapering gas concentrations could also be a symptom of either nutrient or substrate depletion, both of which would limit the rate of methanogenesis.  132  Figure 4.12. Moles of methane entering the column headspace during the ebullition column experiment as a function of the volume of biogenic gas produced. Moles of methane were measured with the OmniStar Gas Analyzer.  Figure 4.13. Moles of methane entering the head space of the column during the column experiment as a function of time. Moles of methane were measured with the OmniStar Gas Analyzer.  133  4.3.8.1.1 Methane as it Relates to the PhreeqC Model  The PhreeqC model is calibrated by relating the gas that enters the experimental column headspace to the amount of gas produced in the modeled OMZ. The total amount of CH4 produced via methanogenesis in the model is 0.02 mols. The total moles of CH4 that accumulate in the headspace of the experimental column is also 0.02 mols. CH4 is stored within the gas bubbles held within the column. The amount of trapped gas in the column is estimated at 185 mL. The PhreeqC simulation suggests that CH4 will constitute close to 50% of the entrapped gas. The number of moles of CH4 that are held within the entrapped gas, and in the dissolved phase of the column are presented in Table 4.12. Henry’s constant implemented in the calculations, at 20 ºC, is 0.0015 [mol L-1] atm-1. The total number of moles of CH4 in the column, ignoring methanotrophic reactions, is computed at 0.023 mols, which is still close to the amount estimated by the PhreeqC calculations. This estimate does not take into consideration mass loss as a result of CH4 oxidation, which is explained in the following section.  Table 4.12. Approximate amount of methane produced and consumed during the course of the column experiment. Simulated  Headspace  Column Bubbles  Dissolved Conc.  Total  Oxygen Consume  Total + Oxygen  Method  PhreeqC  MS  Max / Min  Max / Min  Moles  0.02  0.02  0.0021  0.0003  0.0224  0.0066  0.0290  0.001*  0.00015*  0.0212  0.0046  0.0258  * Calculated by equilibrating moles with headspace volumes  4.3.8.2 Oxygen  O2 is very efficient at oxidizing organic carbon and CH4. The ingress of O2 into the OMZ is minimal; therefore, O2 depletion is mainly attributed to methanogenic reactions. A dramatic increase in the rate of O2 consumption is illustrated in Figure 4.14. CH4 134  oxidation will decrease the total volume of gas in the system. The PhreeqC simulation is based on the total volume of gas exiting the system. Therefore, the volume of gas produced might be underestimated for the reason that CO2 is more soluble than both CH4 and O2.  Figure 4.14. Volume of O2 in the headspace of the column during the column ebullition experiment as a function of time. The theoretical moles of O2, assuming no O2 is consumed are illustrated, as is the predicted volume of moles consumed.  A simple calculation is performed to ensure a large error cannot be attributed to O2 consumption. The total amount of O2 consumed is presented in Figure 4.14. The total consumed volume of O2 in the headspace is 159 mL at initial conditions. If this increase in volume is computed in PhreeqC, the total amount of CH4 produced becomes 0.024 moles. The actual number of moles of CH4 that would be consumed through a methanotrophic reaction is 0.0066 moles. In total, 0.029 moles of CH4 are produced throughout the experiment (Table 4.12). 135  4.3.8.3 Carbon Dioxide  The initial volume of CO2 entering the headspace increases rapidly (Figure 4.4). The headspace volumes of CO2 can, in part, be attributed to methanogenesis; however methanotrophic reactions will also contribute to headspace CO2. The observed sharp rise can be chalked up to the production of CO2 as a result of biodegradation, which occurs on a range of redox reactions; however, because of the initially large CH4 headspace volume it can be assumed that methanogenesis is the dominant redox reaction taking place in the OMZ, even at early times. The CO2 calibration standards yielded low R2 values, and thus CO2 data analysis is omitted from further analysis.  4.3.8.4 Argon  Measured Ar mole fractions along with the theoretical decline in headspace Ar in response to pressure release events are illustrated in Figure 4.15. The measured Ar values are elevated above initial headspace mole fractions as a result of ebullition. Ar contained within the dissolved phase, and stored in bubbles that formed prior to column closure, enters the headspace as ebullition progresses.  136  Figure 4.15. Volume of Ar in the headspace during the column ebullition experiment as a function of time. Mole fractions of O2 were measured with the OmniStar Gas Analyzer. The theoretical decline in headspace argon assuming 0 argon storage in the column is illustrated.  A substantial amount of Ar is measured in the headspace, prior to day 20. A sharp decline of Ar is evident around the 40 day mark. Experimental error might explain this trend. The column may have been disturbed during this time or a preferential release of Ar gas may have occurred, although this is unlikely. The calculated Ar volumes are obtained using weighted averages (Appendix I); this method of approximation may contribute to calculation errors. Alternatively, the rise and fall of Ar can be explained through diffusion along concentration gradients. The ebullition of Ar gas generates elevated headspace Ar partial pressures, so long as the rate of ebullition is greater than the rate of gas release from the column. The equilibrium between the Ar in the headspace and Ar in the dissolved phase is later reestablished through the repartitioning of Ar.  137  4.3.8.5 SF6  The largest total amount of SF6 is measured in the column 17 days post the tracer injection. The total number of moles detected in the headspace at any time, not including gas liberated from the headspace during pressure release events, is 4.4 x 10-5 mols, which is greater than the calculated number of moles injected into the column OMZ. Reasons for the discrepancy include, the partial pressure of SF6 dissolved into the tracer water is in excess of 1 atm, SF6 is preferentially retained within the column headspace during pressure release events, experimental error involving SF6 measurements are large, SF6 does not conform to the laws associated with an ideal gas, measurement error, and finally, a gas bubble, filled with SF6 may have entered the column, along with the tracer water, upon injection. Despite these errors, important information can be gained through the analysis of the tracer test.  Figure 4.16. Moles of SF6 in the column headspace during the column ebullition experiment. Moles of SF6 are measured with the OmniStar Gas Analyzer.  138  The PhreeqC simulation suggests that the majority of SF6 partitions into the entrapped OMZ gas immediately, which is expected based on the low solubility. The onset of ebullition occurs prior to the SF6 injection event and so the column at the time of injection is mostly saturated with bubbles. SF6 is first detected 2 days after the injection; therefore, the fastest rate of travel for a bubble, can be estimated at 2 days. The majority of SF6 enters the headspace by the 16th day.  For an open system, such as a permeable vadose zone, if a bubble crosses the water table and releases SF6 to the vapor phase, the diffusion of SF6 away from the point of bubble entry will be relatively slow in comparison to other gases. SF6 is a very large molecule, with a very low diffusion coefficient of 6.1 x 10-2 cm2 s-1, in air (Vulava et al., 2002). This low diffusion coefficient might increase the effectiveness of SF6 as a tracer in the vadose zone, so long as the instrument detection limits are sufficiently low and that the point of bubble entry into the vadose zone is known. However, the solubility of SF6 in the tracer water limits its effectiveness as a tracer gas. SF6 is a suitable ebullition tracer in capped headspace environments; however, it is not recommended for open headspace systems.  4.4  Conclusion  Significant carbon mass loss can occur through ebullition. The storage of gas in the sediment can reach a pseudo-steady state early on in the experiment. The column likely continues to store gas, but to a much smaller degree, after maximum gas saturation volumes are reached. Gas tracers are ideal tools for ebullition detection. The column experiment infers that if ebullition is to be monitored over a long period of time under closed system conditions, Ar (or heavier noble gases) will be the most suitable tracer, as it will remain in the OMZ for a longer period of time and is present at measurable atmospheric levels. The low solubility of SF6 will ensure that repartitioning of the tracer gas through the saturated medium will be minimal. The instrumentation for SF6 detection should have a relatively low detection limit. The effectiveness of SF6 as a 139  tracer can be seriously impeded by the presence of hydrocarbons in the system, as well as by the amount of gas that exits the system during an individual headspace reading. Caution should be taken when implementing SF6 in the evaluation of ebullition, and it is recommended only for closed headspace experiments.  140  5  5.1  Relating Saturated and Unsaturated Gas Transport Mechanisms in a Hydrocarbon Contaminated Setting  Introduction  The behavior of nonreactive gases, in the presence of biogenic gas, has thus far been investigated in, the vadose zone (Chapter 2), the dissolved pore water (Chapter 3), and under laboratory conditions (Chapter 4). The intricate relationship between mass transport in the saturated zone pore water and the overlying vadose zone in field settings has yet to be explored. An investigation into the links relating dissolved nonreactive gas concentrations to the overlying gas phase will ensure that results are cohesive on all fronts. Significant laboratory findings will be applied to field settings; however, the bulk of this chapter will focus on the noble gas measurements obtained at the Bemidji Site. Ebullition will be evaluated through empirical evidence and later supplemented by additional DGM modeling efforts, in the vadose zone. An unabridged detailing of the gas transport processes within the subsurface will help to refine estimates associated with the rate of natural attenuation of the contaminated aquifer.  5.2  Applying Laboratory Findings to the Field Site  5.2.1 Physical Column Measurements Applied to Bemidji Field Data  During the column experiment, the ebullition of gas through the sediment of the column into the headspace was significant. The largest headspace pressure increases associated with ebullition transpired during pressure release events. This suggests that pumping within the vadose zone, or barometric pumping, may promote pressure changes, which in turn might catalyze ebullition in the field. The rate of volume increase of gas into the headspace reached a constant value early on in the experiment timeframe; the volume of entrapped column gas reached a maximum saturation level 141  within the first 30 days of the column experiment. These findings help to validate the constant gas saturation approximation implemented during the ebullition modeling in Chapter 3.  5.2.2 Potential of SF6 as a Gas Tracer at Bemidji Site  The presence of hydrocarbons at the Bemidji site will impede the effectiveness of SF6 as a dissolved gas tracer, as it will diminish the concentration of SF6 that reaches the vadose zone. The SF6 will partition into the entrapped gas phase at the Bemidji site. Approximately 1 mL of the entrapped gas phase escapes per liter of pore water per day. At these levels, SF6 would not be a suitable point source tracer for ebullition in the presence of hydrocarbons.  5.2.3 Argon Comparisons  An important finding, established in both the OMZ PhreeqC simulations and the Lagrangian style ebullition modeling, pertains to the relationship between Ar and the heavier noble gases. Comparisons are drawn between modeled Ar values obtained under either a degassing-only constraint or within the confines of an ebullition-controlled regime. Models pertaining to the field settings of the shallow unconfined aquifer (Chapter 3), calculate Ar values in excess of observed concentrations at the site, unless an ebullition approach is adopted towards the system, in which case the model results accurately predict Ar dissolved concentrations. The same trend is apparent in the noble gas data set calculated during the PhreeqC OMZ simulation, in Chapter 4. The OMZ is largely stripped of all dissolved non-biogenic gases but nonetheless, the modeled Ar concentrations approach Xe values with successive ebullition events. This signal diminishes when a degassing model is applied to the OMZ. It can, therefore, be suggested that the Ar/Xe ratio will be substantially decreased relative to atmospherically equilibrated water, in an ebullition setting. 142  5.3  Coupling of the Ebullition Flux to Vadose Zone Gas Transport at the Bemidji Site  5.3.1 Coupling of the Biogeochemical Reaction Zones at the Site  The following data analysis, couples gas transport in pore water, through ebullition, to the vadose zone. From Figure 5.1 it is evident that the methanogenic and methanotrophic zones within the subsurface are related to the position of the LNAPL, therefore, the analysis is limited to source zone locations. The silt layer at the site extends well into the LNAPL but does not significantly intersect the vadose zone. It can accordingly be assumed that vadose zone gas transport can be applied across the extent of the free phase product in locations above the north pool.  143  Figure 5.1. A cross section intersecting the extent of the Bemidji site positioned along the axis of the north plume detailing the position of the vapor wells and monitoring wells that are sampled during noble gas analysis, the position of the LNAP, the location of the methanotrophic and methanogenic zones, and the relevant site geology.  5.3.2 Empirical Evidence Supporting Ebullition with the Dissolved and Vapor Phase Noble Gases  Chapter 3 establishes that noble gases in the vadose zone and noble gases in the pore water are not in equilibrium. Ebullition modeling results support the supposition that ebullition is ensuing at monitoring well 315. The presented noble gas ratios suggest that degassing, and possibly ebullition, is occurring at other source zone locations (534B, 532A). To reiterate, in the pore water, heavier noble gases are enriched relative to lighter gases, reducing the noble gas ratio relative to atmospheric 144  levels. The vapor wells, sampled above the free product, indicate the inverse relationship. An ebullition flux would augment the noble gas ratios in the vadose zone; however, the noble gas signal must be distinguished from vadose gas transport signals. Empirically related Ar/Xe ratios are used to estimate the potential for ebullition through the comparison of the vadose zone values to the dissolved values. Ar/Xe ratios and well couplings are summarized in Table 5.1 and illustrated in Figure 5.2.  Table 5.1. Ar/Xe ratios in both the dissolved and vapor phases at the Bemidji site Vapor well Mon. Well (Ar/Xe)vadose Err (Ar/Xe)vadose (Ar/Xe)saturated Err (Ar/Xe)saturated 310G-1  310E  1.1E+05  2.0E+03  2.8E+04  8.2E+02  532G-1  532A  1.1E+05  2.2E+03  2.0E+04  5.7E+02  533B  533B  1.0E+05  1.7E+03  2.5E+04  6.3E+02  534G-1  534B  1.2E+05  2.3E+03  2.3E+04  6.2E+02  9016G-1  315  1.2E+05  2.4E+03  1.2E+04  3.0E+02  145  Figure 5.2. Ar/Xe ratios of noble gas mole fractions in the vadose zone plotted against dissolved concentrations in the saturated zone in monitoring and vapor well couplings located along the axis of the north plume. Monitoring wells are indicated on the figure.  Smaller Ar/Xe ratios are associated with greater rates of gas exsolution, which increases the likelihood of ebullition, as the dissolved Ar becomes progressively depleted with respect to the more soluble Xe. Ar/Xe values sampled from source zone wells are lower than Ar/Xe values measured at background well 310 (Figure 3.12). Figure 5.2 shows a negative correlation between dissolved and vadose zone Ar/Xe values. Identical trends are noted for Ne/Xe, Ne/Kr, and Ar/Kr ratios, measured at the site. The difference between the ratios obtained in the vadose zone and in the dissolved pore water, is the most pronounced at the 315-9016 well coupling, located in the centre of the source zone. If bubbles enter the vadose zone, the Ar/Xe ratio will increase, so long as the saturated zone is constantly replenished with noble gases, for the reason that the entrapped gas bubbles will contain a larger proportion of lighter 146  gases due to their lower solubility, as observed in Figure 2.9. This alone is a strong line of evidence to support ebullition, save for the fact that all source zone lower vapor ports will also be enriched in lighter gases relative to heavier gases, as a result of gas cycling through the vadose zone.  5.3.3 Relating the MIN3P-DGM Modeling Results to the Ebullition Model Results  Modeling efforts applied to both the vadose zone and the saturated zone at the Bemidji site are used to determine the rates of CO2 and CH4 gas production. A 30 cm smear zone of residual LNAPL is located directly above the water table at well 601. This implies that not all of the biogenic gas production in the unsaturated sediment, if any, originates from gas bubbles crossing the water table, as decay processes will also be occurring in the vadose zone. The ebullition flux must therefore be less than the gas rates applied to the MIN3P-DGM modeling. Portions of the biogenic gas added to the ebullition model will remain dissolved in the groundwater, and so gas ebullition fluxes, based on total gas production rates may overestimate the actual amount of gas exiting the saturated zone through ebullition. However, the modeling results assumes that ebullition only occurs to a depth of 60 cm, when in reality, methanogens are present in significant concentrations at depths up to 1 m beneath the water table (Bekins et al., 2001).  The PhreeqC data output files, associated with the ebullition model, also provide an estimate of the amount of moles exiting the system, so long as the ideal gas law is imposed on volume measurements. Further to this, the moles can be subdivided into their molecular components. The moles of CO2 and CH4, contained within a specified volume of upwards migrating gas, are calculated at the site. A summary of the potential modeled flux of biogenic gas crossing the water table and entering the vadose zone through ebullition, as calculated by both the MIN3P-DGM model and the ebullition model, is provided in Table 5.2. 147  Table 5.2. A comparison of the possible ebullition flux as calculated by the MIN3P-DGM model and the ebullition model Ebullition Model Ebullition Model Layered DGM Model Biogenic Rate Moles Exiting Bubble Gas Model Rate (mol s-1) Volume Producing Gas (L) Total Production (mol s-1) Domain Boundary Area (m2) Ebullition Flux (mol m-2 s-1) % of DGM Model Flux  CH4  CO2  CH4  CO2  CH4  CO2  6.0E-9  4.0E-9  50  50  4  4  3.0d-7  2.0d-7  1.19E-9  1.19E-9  1.42E-9 4.16E-10  1  1  0.0225  0.0225  0.0225  0.0225  3.0d-7  2.0d-7  5.27E-8  5.27E-8  6.31E-8  1.85E-8  100  100  17.6  26.3  21.0  9.3  2.96E-10 2.96E-10 3.56E-10 1.04E-10 4  4  *Values calculated as 0.125 % of gas bubble composition for the 20% gas saturation ebullition model results.  The potential flux of gas attributed to ebullition is quite substantial but the ebullition flux does not account for the total rate of biogenic gas production calculated in the vadose zone. Ebullition fluxes are calculated as percents of the biogenic gas production rate, as simulated by the MIN3P-DGM model. The flux of CH4 entering the subsurface ranges between 17.6 % and 21 % of the total maximum vadose zone gas flux; the ebullition flux associated with CO2 is much more variable, brought about by the high solubility of carbonates in solution. The CO2 flux of gas, accredited to the gas production rate entered into the ebullition-modeling domain, will most likely over estimate the potential CO2 ebullition flux values. The calculated flux values must be consigned to additional vadose zone MIN3P-DGM modeling efforts to further constrain estimates.  148  5.3.4 MIN3P-DGM Model - Noble Gas Component and an Inclusive Ebullition Flux  5.3.4.1 Ebullition Flux  MIN3P-DGM modeling focuses on vadose zone gas transport at vapor well 601. The ebullition flux is incorporated into the model to simulate gas additions as a result of bubbles crossing the water table. The conceptual model is outlined in Figure 5.3.  Figure 5.3. Conceptual model applied to vadose zone gas transport with an inclusive ebullition component incorporated into the model at vapor well 601.  149  To simulate ebullition in the model, a source term is added to the lowest cell in the domain. The composition of the gas flux is approximated from the data provided in the output file of the ebullition model at steady state - 20% gas saturation (Chapter 3). The estimated total flux of gas entering the DGM grid is an estimate of the total molar ebullition flux associated with the ebullition model. The proportion of each gas species entering the model domain and the total flux of gas into the system is summarized in Table 5.3.  Table 5.3. Summary table of the values used to calculate the theoretical nonreactive gas composition of the source term implemented during MIN3P-DGM modeling Gas Ebullition % Added to Mass in Rate Added Rate Inserted in Amount* Source Source Flux to Model** Input File*** (mol (mols) Flux (g) (mol m-2 s-1) L(bulk)-1 s-1) He  5.49E-09  1.12E-6  4.48E-06  Ne  1.76E-08  3.59E-06  7.18E-05  Ar  1.78E-05  3.64E-03  1.46E-01  N2  9.09E-04  1.86E-01  5.20E-00  Kr  2.92E-09  5.97E-07  5.01E-05  Xe  2.50E-10  5.11E-8  6.74E-06  CO2  8.99E-04  1.83E-01  8.07E+00  CH4  3.07E-03  6.27E-01  1.00E+01  Model  4.90E-03  1.00E-00  2.35E+01  * **  ***  1.01E-07  1.01E-08  Calculated as 12.5% of the moles present within the gas phase of the ebullition modeling calculated at a gas saturation level of 20% Total molar increase of gas contributing to ebullition for the ebullition model at 20 % gas saturation. The domain boundary area through which the moles pass is (0.0225 m2); however the rate is presented in terms of m2. Accounts for the 10 L volume of the mineral phase in the model  150  5.3.4.2 Model Parameters The aquifer properties applied to the current model are identical to those outlined for the layered heterogeneous simulation in Chapter 2. The only modification to the input file is the calibrated biogenic gas production rates and the introduction of the ebullition source term. Initially, modeling efforts focused on a homogenous subsurface. Extensive modeling was conducted in both a single and layered heterogeneous regime; however, the gas profiles obtained in the heterogeneous system most accurately represented the observed noble gas values. The aquifer properties are outlined in Table 5.4.  Table 5.4. Assigned aquifer property variables at profile 601 implemented in MIN3P-DGM modeling, with an inclusive ebullition flux Aquifer Property  Simulation with Ebullition  Porosity  0.38 / 0.33  K (m s-1) from 0-3 m  5.0 x 10-5  K (m s-1) from 3-6.55 m  3.0 x 10-6  Van Genuchten, alpha (m-1)  3.00  Van Genuchten, n  1.60  Residual Saturation  0.05  CH4 Rate (mol l-1s-1)  1.2 x 10-8 (1.2 x 10-7)*  CO2 Rate (mol l-1s-1)  4.5 x 10-9 (4.5 x 10-8)*  Ebullition Flux (mol l-1s-1)  8.0 x 10-9 (8.0 x 10-8)*  % CH4 Ebullition Flux of total** CH4 Flux  29  % CO2 Ebullition Flux of total** CO2 Flux 24 2 *Total Amount Per m **Indicated inputted rate plus % rate of that species in the ebullition flux  The rates of CH4 and CO2 production are less than the rates implemented in the initial modeling efforts detailed in Chapter 2. The CH4 attributed to ebullition is 29% of the total calibrated CH4 production rate in the vadose zone; whereas, the CO2 ebullition  151  flux contributes to 24% of the total amount of CO2 produced. The biogenic ebullition contributions to each respective flux are almost equivalent, post calibration efforts.  5.3.5 MIN3P-DGM Discussion for Profile 601, with Ebullition Considerations  The ebullition flux does not alter the influence permeability exerts over gas calibration, when ebullition constitutes between 0 % and (approximately) 25% of the total biogenic gas production rate in the model domain; noble gas profiles obtained for ebullition rates greater than (approximately) 25 % cannot be constrained to observed values (not shown). The calibration of major component gas profiles can be achieved for ebullition rates that contribute up to 48% of the bulk gas production within the model domain. The CO2 and CH4 gas rates were calibrated independently of the ebullition flux. Vadose zone modeling can, therefore, not be used to quantify a possible ebullition flux; ergo, current modeling efforts only support the theory of ebullition, but cannot act alone as an indicator of ebullition.  Model calibration of major component gases can be achieved for models that both preclude and include an ebullition flux. This is likely because the biogenic gases constitute the majority of the ebullition flux. The calibrated major gas components are presented in Figure 5.4. N2 values are underestimated for both sets of modeling results. The reason for this is likely a combination between measurement error and slight inaccuracies associated with the model calibration.  152  Figure 5.4. Vertical profile of modeling results and field measurements for major component gas mole fractions, at monitoring well 601 in a layered heterogeneous subsurface. An ebullition flux is included in the model calibration. Noble gas profiles are presented in Figure 5.5. Modeling results do not differ greatly from the previously attained profiles in Chapter 2; however, they are constrained to the specified biogenic and ebullition fluxes entered into the model. Noble gas concentrations are the best indicators of subsurface permeability, as noble gas calibration could not be achieved under a homogenous system; however, they cannot be used alone to evaluate ebullition.  153  Figure 5.5. Vertical profile of modeling results and field measurements for noble gas mole fractions, at monitoring well 601 in a layered heterogeneous subsurface. An ebullition flux is included in the model calibration.  Major component gas transport at vapor well 601, for a layered heterogeneous vadose zone, with an inclusive ebullition component, is almost identical to simulations that neglect ebullition (Figure 5.6). The inwards diffusive flux of O2 is slightly greater when ebullition is considered. The upward advection component to flow for both of the biogenic gases increases, as does the diffusive upward component; however, for the most part the pattern associated with flow rates is comparable, and flow discrepancies can be attributed to the accuracy of the calibration.  154  Advection Diffusion DGM Nonequi  Figure 5.6. Veritical profiles of the advective, diffusive, non-equimolar and DGM flux at vapor well 601 in a layered heterogeneous subsurface. An ebullition flux is included in the model calibration. Plots illustrate system fluxes for O2, CH4, CO2, Ne, and Xe, respectively.  The flux diagrams presented for the noble gases differ from the profiles presented in Chapter 2. The upward advective flux does not equal the downward diffusive flux for gas flow at regions beneath the area of gas consumption (methanotrophic zone). The heavier molecules show the most prevalent divergences between advection and counter diffusion. The diffusion coefficient for the larger noble gases is smaller than that of the lighter gases, confirming again that heavier gases are the most apt at predicting areas of gas consumption and depletion in the vadose zone. Flow of gas 155  above the methanotrophic zone is also altered such that the inwards advection is much less than the outwards diffusion.  5.4  Conclusion  Low Ar/Xe ratios, in comparison to background values, are detected throughout the source zone in the saturated pore space, and correlate to high Ar/Xe ratios sampled from vapor wells located directly above the water table. Gases in the unsaturated sediment will be subject to the gas transport principles associated with the vadose zone. MIN3P-DGM vadose zone modeling can be calibrated to varying amounts of ebullition fluxes entering the vadose zone, up to (approximately) 25% of the total carbon flux through the system. As a result of gas flow through the unsaturated pores, vadose zone monitoring in shallow unconfined aquifers cannot be used alone to predict ebullition and must be coupled with dissolved gas analysis. The vadose zone noble gas values cannot be calibrated to a flux that is greater than (approximately 25 %) of the total production rate, and therefore ebullition cannot account for all of the carbon traveling through the vadose zone.  156  6  Summary and Conclusions  The behavior of nonreactive gases in the saturated and unsaturated zones of a petroleum-hydrocarbon contaminated unconfined aquifer has been the focal point of this thesis. The effectiveness of naturally occurring nonreactive gases as indicators of transport processes, biogeochemical reaction zones, and the occurrence of ebullition, was evaluated through noble gas analyses and reactive transport modeling, conducted in Chapter 2 and Chapter 5. Chapter 3 explored the potential of noble gases, dissolved in the saturated pore water of a shallow unconfined aquifer, to predict rates of biogenic gas formation, and of ebullition. The effectiveness of the point source ebullition tracer, SF6, injected into the sediment of a closed column, was examined along side the partitioning behavior of SF6 into hydrocarbons, in laboratory experiments, detailed in Chapter 4. Chapter 5 attempted to relate the above Chapters, linking vadose zone gas compositions to dissolved gas concentrations. The pertinent findings procured throughout the thesis are summarized below.  The results obtained from noble gas sampling, conducted in the vadose zone of the Bemidji aquifer, support and enhance previous datasets obtained at the site. The noble gas data corroborates the hypothesis that areas of gas consumption are enriched in nonreactive gases; whereas, zones of gas production are marked by depletions in the nonreactive gases, as a result of the gases entering or exiting the respective zones through a pressure induced advection flux. The diffusive flux of noble gases within the vadose zone is mass dependent. This relationship can be exploited to more clearly illustrate the interactions between diffusive and advective vadose zone gas fluxes. The noble gas profiles show that heavier noble gases will become more concentrated than the lighter noble gases in methanotrophic zones, which is characterized by reactive gas consumption. This can be explained by the greater diffusion coefficients of lighter gases in relation to the heavier gases, allowing the smaller molecules to diffuse away 157  from reaction zones the fastest, and diluting their signal. The same holds true for methanogenic gas formation zones, where the largest signals, in this case depletion relative to atmospheric values, are found in heavier noble gases. Over all, the largest molecules, consequently with the lowest diffusion coefficients, are the best predictors of pressure-induced flow within the unsaturated pore space. The elemental mass fractionation observed in the vadose zone also implies that pressure differences throughout the subsurface, as a result of biogeochemical reactions, are easily mitigated through the flux of gas into said areas.  The gas compositions sampled along defined profiles in the vadose zone can be substantiated through MIN3P-DGM reactive transport modeling. The noble gas modeling results further validate previous findings, obtained by Molins et al. (2009). The mass dependency of the noble gas diffusion coefficients, as calculated in the MIN3P-DGM code, support the hypothesis that Kr and Xe gases in the vadose zone are more efficient at tracking reactions zones within the subsurface than are the lighter noble gases.  This mass dependent tracer suitability was not previously established  with major component gas sampling.  The concentration of dissolved noble gases in the pore water, beneath the water table, can be used to empirically estimate gas exsolution at the site. Due to their lower solubility in water, the lighter gases will preferentially partition into the entrapped gas bubbles. The saturated pore water will become depleted in noble gases relative to atmospheric concentrations, and elemental fractionation of the gas will ensue, resulting in an enrichment of heavier gases in the pore water relative to lighter gases, as a result of solubility controls. The degree of gas exsolution, across the extent of the plume, can be qualitatively compared through the analysis of noble gas ratios.  Modeling results support the hypothesis of ebullition at the Bemidji site. The degree of pore water gas exsolution can be estimated using the ebullition modeling 158  technique, as described in Chapter 3. Modeling results suggest that gas generation in the source zone, in the vicinity of monitoring well 315, is estimated at 5.78 x 10-10 mol Lpore water-1s-1. The minimum amount of gas crossing the water table as a result of methanogenesis is approximated at 0.177 L m-2 day-1. The modeling results suggest that at steady state, pore water will exhibit identical dissolved gas concentrations, and biogenic gas formation rates, independent of the maximum gas saturation volume of the sediment pore space, provided that ebullition is occurring. The modeling results should not be taken as a finite estimate towards the ebullition flux and gas production rates at the Bemidji site. The assumptions and uncertainties related to the modeling results remain large and model refinement is required before definite statements can be made in regard to carbon fluxes within the system. Despite these limitations, the modeling results strongly indicate that ebullition is occurring at the site, and that ebullition can help to explain the attenuation of the observed CH4 plume, relative to groundwater flow velocities.  Ebullition rate estimates can range up to 25% of the observed carbon flux in the vadose zone; however, this value cannot be constrained through vadose zone MIN3PDGM modeling. So long as transportation processes are ongoing in the vadose zone, the noble gas composition of the unsaturated pores alone cannot be used to indicate ebullition. Vadose zone results must be coupled with dissolved gas analysis.  An additional and unforeseen outcome of the study pertains to the phenomenon of excess air, which is evaluated at background well 310. The results of the vadose zone monitoring at vapor well 310 indicate increases to the nonreactive gas partial pressures at locations above the water table. This suggests that excess air, explained as: the over pressuring of dissolved noble gases in groundwater samples, as well as a mass fractionation pattern wherein heavier gases are enriched relative to lighter gases, may in part be attributed to transport processes occurring within the vadose zone. A possible explanation for this is that the consumption of gas within the vadose zone will lead to increases in the partial pressures of constituent gases, which in turn will 159  augment the amount of each gas that partitions into solution. Furthermore, the gas fractionation might be attributed to the diffusive differences inherent to each individual noble gas.  Diffusion within the vadose zone complicates the effectiveness of ebullition gas tracers, when gas sampling occurs at locations above the water table. This problem can be eliminated in closed environments, such as column experiments. The detection of biogenic gases in the column headspace can indicate ebullition; however, reactive gases can be consumed, or produced through an array of redox and geochemical reactions. Nonreactive gases can also act as tracers for ebullition in the headspace of a column experiment. The injection of anthropogenic gases into the dissolved pore water, and their subsequent detection in the headspace, suggests that gas tracer injections can be used to determine ebullition. The limitation connected with gas injections pertains to its dependency on the rate of ebullition and the ability of the overlying gas phase to entrap the tracer gas in significant concentrations before diffusion occurs. Furthermore, equilibrium between the tracer water and the perturbed environment may diminish its productiveness as a gas tracer.  As a final note, the success of an injected ebullition tracer gas that is not in equilibrium with the vadose zone depends on the type of contaminant present within the system. Generally, nonreactive gases are nonpolar by nature, thus if the contaminant consists of an immiscible phase, it will probably be nonpolar. As a result, the tracer will likely be more soluble in the contaminant than it is in the groundwater. An evaluation of the nature of the contaminant should be critically examined prior to nonreactive gas tracer injections.  The applicability of this study extends farther than to just hydrocarbon contaminated sites. Vadose zone measurements directly above the water table will increase the accuracy involved with the analysis of dissolved gas concentrations and should be implemented, when possible, if sampling noble gases in unconfined aquifers. 160  Identifying reaction zones within the subsurface will facilitate its biogeochemical delineation, so long as a gas is produced or consumed within the subsurface. This method of approximation can be applied to waste rock piles, where O2 is consumed as a result of pyrite oxidation.  Vadose zone noble gas measurements can be implemented at various contaminated sites, but cannot alone be used to identify ebullition. Dissolved noble gas measurements are much more applicable than vadose zone gases when it comes to ebullition. The dissolved concentrations are a function of the rate of gas production, so long as the system has reached steady state. The rate of ebullition can be estimated in unconfined aquifers if dispersion is minimal during gas analysis, as the modeling is Lagrangian in nature, and so long as the flow path can be identified. The approach works best for methanogenic zones located directly under the water table. When modeling is concerned, the heavier ratios will reach a steady state in advance of the lighter gases, and so future ebullition modeling should center on heavy noble gas calibration. Model development for ebullition remains in preliminary stages; much refinement is needed before estimates regarding gas production rates and ebullition fluxes can be calculated with minimal uncertainty. Permeability variations with depth, as well as a more accurate approach towards diffusive fluxes, should also be applied to model modifications.  It is recommended that future modeling efforts, pertaining to an ebullition flux, should adopt the Lagrangian steady state approach and implement these findings in a controlled study, whereby gas production rates are fixed, or major gas component concentrations are known. It is suggested that future studies should focus on additional column experiments. The dissolved concentrations of the column should confirm the accuracy of the ebullition model. As an extension to the current column experiment, injections of SF6 in areas of ebullition free from hydrocarbons, would substantiate the usefulness of SF6 as a tracer in field settings. It would also help to further evaluate the potential effect vadose zone gas transport exerts over noble gas concentrations. Overall, the implementation of nonreactive gases in the analysis of contaminated 161  sediments will help to refine gas transport processes. 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Major component gas dataset for vadose zone gas analyzed with the CP-4900 Varian gas chromatograph during 2008 sampling event, Bemidji, Minnesota Port  Ar%  O2%  N2%  CH4%  CO2 %  Total Atm.  21-Jul  7  0.930  20.1547  77.756  0.0060  0.5965  0.9944  21-Jul  6  0.929  20.0871  77.735  0.0000  0.6347  0.9939  21-Jul  5  0.927  19.9237  77.511  0.0000  0.6748  0.9904  21-Jul  4  0.931  19.4978  77.892  0.0604  0.8496  0.9923  21-Jul  3  0.942  18.8796  78.818  0.0604  1.2083  0.9991  21-Jul  2  0.940  18.4931  78.642  0.0604  1.3746  0.9951  21-Jul  1  0.938  18.5258  78.464  0.0604  1.3858  0.9938  21-Jul  7  0.930  20.0302  77.769  0.0609  0.6927  0.9948  21-Jul  6  0.927  19.9381  77.564  0.0603  0.7806  0.9927  21-Jul  5  0.928  19.7926  77.586  0.0000  0.9181  0.9923  21-Jul  4  0.936  18.9785  78.260  0.0000  1.3632  0.9954  21-Jul  3  0.954  16.3643  79.753  0.0000  2.8335  0.9991  21-Jul  2  0.952  16.5576  79.587  0.0605  2.7074  0.9987  21-Jul  1  0.943  17.8303  78.876  0.0605  2.1323  0.9984  21-Jul  7  0.931  19.9620  77.855  0.0605  0.7560  0.9957  21-Jul  6  0.928  19.5796  77.611  0.0605  1.0086  0.9919  21-Jul  5  0.929  19.2749  77.712  0.0606  1.2401  0.9922  21-Jul  4  0.944  16.4208  78.989  0.0606  2.7868  0.9920  21-Jul  3  0.979  10.7748  81.916  0.0614  6.5246  1.0026  20-Jul  2  0.967  10.2022  80.910  0.0000  6.9569  0.9904  Well/Sampling Date 531  518  532  169  Well/Sampling Date  Port  Ar%  O2%  N2%  CH4%  CO2 %  Total Atm.  21-Jul  9  0.931  19.7772  77.909  0.0604  0.8493  0.9953  21-Jul  8  0.922  19.3540  77.089  0.0604  1.0244  0.9845  21-Jul  7  0.926  18.6323  77.416  0.0604  1.5026  0.9854  21-Jul  6  0.950  15.0669  79.498  0.0604  3.6408  0.9922  21-Jul  5  0.993  6.1193  83.021  0.0605  10.055  1.0025  21-Jul  4  1.000  4.9485  83.663  0.0606  10.575  1.0025  21-Jul  3  1.011  3.6195  84.531  0.0606  11.962  1.0118  21-Jul  2  0.998  1.6835  83.444  0.3503  13.666  1.0014  21-Jul  7  0.930  20.0941  77.756  0.0000  0.4520  0.9923  21-Jul  6  0.929  19.7704  77.711  0.0000  0.9704  0.9938  21-Jul  5  0.927  19.2714  77.519  0.0604  1.3465  0.9913  21-Jul  4  0.976  10.7047  81.630  0.0605  6.9659  1.0034  21-Jul  3  1.028  0.9710  85.939  0.0654  13.640  1.0164  21-Jul  2  1.012  0.2653  84.602  1.6873  14.559  1.0213  21-Jul  1  0.965  0.3096  80.709  5.2719  14.969  1.0223  21-Jul  7  0.936  18.1721  78.289  0.0712  2.2933  0.9976  21-Jul  6  0.974  10.9811  81.488  0.0000  7.2877  1.0073  21-Jul  5  1.010  4.0188  84.511  0.0614  11.899  1.0150  21-Jul  4  1.018  0.3537  85.182  0.5026  14.624  1.0168  21-Jul  3  0.970  6.7189  81.165  0.9501  10.710  1.0052  21-Jul  1  0.934  15.8682  78.114  0.8098  4.0456  0.9977  20-Jul  6  0.924  18.3853  77.31  0.00  1.84  0.98  20-Jul  5  0.950  12.5500  79.42  0.00  6.10  0.99  20-Jul  4  0.983  5.0170  82.18  0.00  11.54  1.00  20-Jul  3  0.986  0.5035  82.47  1.23  14.66  1.00  9101  533  9103  534  170  Well/Sampling Date  Port  Ar%  O2%  N2%  CH4%  CO2 %  Total Atm.  20-Jul  2  0.973  0.2869  81.35  3.83  14.92  1.01  20-Jul  1  0.865  0.2346  72.35  14.25  16.09  1.04  20-Jul  7  0.919  18.6706  76.86  0.00  1.84  0.98  20-Jul  6  0.923  17.7666  77.20  0.00  2.65  0.99  20-Jul  5  0.940  14.1797  78.61  0.00  5.38  0.99  20-Jul  4  0.996  0.2934  83.32  1.42  14.91  1.01  20-Jul  4  0.994  0.3056  83.13  1.42  14.88  1.01  20-Jul  3  0.977  0.2427  81.70  3.93  14.82  1.02  20-Jul  2  0.868  0.2520  72.57  14.44  15.62  1.04  20-Jul  1  0.819  0.2376  68.50  20.11  16.35  1.06  20-Jul  1  0.811  0.1932  67.82  20.10  16.37  1.05  22-Jul  8  0.945  14.4865  79.020  0.1004  5.6949  1.0025  22-Jul  7  0.967  6.9644  80.898  2.0985  10.170  1.0110  22-Jul  6  0.981  0.3765  82.063  5.1704  13.999  1.0259  22-Jul  5  0.973  0.3760  81.349  6.2923  14.049  1.0304  22-Jul  4  0.914  0.2693  76.433  14.494  11.622  1.0373  22-Jul  3  0.806  0.2260  67.460  20.967  15.514  1.0498  22-Jul  2  0.751  0.2497  62.814  25.085  16.012  1.0491  22-Jul  1  0.746  0.2178  62.445  25.557  16.186  1.0515  22-Jul  8  0.948  12.8613  79.279  0.0935  6.9612  1.0014  22-Jul  7  0.963  7.8963  80.546  0.0938  11.371  1.0087  22-Jul  6  0.982  0.2853  82.117  0.8013  18.137  1.0232  22-Jul  5  0.965  0.3766  80.744  1.5633  18.001  1.0165  22-Jul  4  0.948  0.2750  79.290  7.3579  15.440  1.0331  22-Jul  3  0.948  0.2968  79.254  8.5107  14.419  1.0343  601  9014  9015  171  Well/Sampling Date  Port  Ar%  O2%  N2%  CH4%  CO2 %  Total Atm.  22-Jul  2  0.892  0.2213  74.597  13.616  14.513  1.0384  22-Jul  1  0.879  0.2745  73.542  14.456  14.638  1.0379  22-Jul  8  0.930  18.3393  77.81  0  2.37  0.9945  22-Jul  7  0.934  16.5253  78.140  0.0000  3.6600  0.9926  22-Jul  6  0.928  15.7817  77.610  0.0000  4.3200  0.9864  22-Jul  5  0.928  15.3113  77.640  0.0900  4.9500  0.9892  22-Jul  4  0.931  13.7484  77.880  0.1000  6.3300  0.9899  22-Jul  3  0.889  0.2201  74.400  11.800  14.640  1.0195  22-Jul  2  0.894  0.2458  74.760  11.290  14.580  1.0177  22-Jul  8  0.934  17.2552  78.150  0.0000  3.2300  0.9957  22-Jul  7  0.953  14.1367  79.700  0.0000  5.9200  1.0071  22-Jul  6  0.964  8.3859  80.600  0.0000  10.870  1.0082  22-Jul  5  0.966  8.3140  80.760  0.0000  10.860  1.0090  22-Jul  4  0.934  0.2660  78.080  7.0200  16.090  1.0239  22-Jul  3  0.928  0.3120  77.580  8.6800  15.820  1.0332  22-Jul  2  0.917  0.2322  76.730  9.3800  15.860  1.0312  22-Jul  7  0.931  19.0682  77.900  0.0000  1.6400  0.9954  22-Jul  6  0.937  17.1626  78.370  0.0000  3.3600  0.9983  22-Jul  5  0.939  16.2510  78.500  0.1000  4.1800  0.9997  22-Jul  4  0.893  0.2465  74.700  12.140  14.980  1.0296  22-Jul  3  0.891  0.2583  74.550  12.490  15.030  1.0322  22-Jul  2  0.870  0.3197  72.760  13.720  15.050  1.0272  22-Jul  2  0.934  20.5327  78.124  0.0000  0.3244  0.9992  22-Jul  1  0.923  20.4832  77.224  0.0930  0.3488  0.9907  9016  9017  604  310  172  Figure A.1. The vapor well locations of wells sampled for major component gas analysis. All wells are located along the axis of the north plume.  173  Appendix B Table B.1. Noble gas dataset for vadose zone gas analyzed through noble gas extraction lines and mass spectrometry at EAWAG during 2008 sampling event, Bemidji, Minnesota Vapor  He (cc/cc)  He Err  Ne (cc/cc)  Ne Err  601-5  4.66265E-06  5.4628E-08  5.96086E-06  6.7679E-08  601-7  6.021E-06  Ar (cc/cc)  Ar Err  Kr (cc/cc)  Kr Err  Xe (cc/cc)  0.007457541 7.70453E-05 9.36439E-07 1.21021E-08 7.10078E-08 1.32114E-09  6.65344E-08 1.82734E-05 2.07359E-07 0.009400282 9.71033E-05 1.14427E-06 1.49484E-08 8.81282E-08  5.80513E-06 6.41504E-08 1.85517E-05  601-3  5.30435E-06 6.57863E-08 1.84002E-05 2.08702E-07 0.009341715 9.65627E-05 1.14581E-06 1.47708E-08 8.66424E-08 1.35227E-09  601-4 532G-2  5.38028E-06 5.94673E-08  1.9016E-05  2.15748E-07  0.009205302  0.00969219  5.38091E-06 6.67442E-08 1.92038E-05 2.17847E-07 0.010107934  9.508E-05  1.4813E-09  601-6  310G-1  2.1045E-07  Xe Err  1.14856E-06 1.55733E-08 8.67064E-08 1.94079E-09  0.000100155 1.19009E-06 1.52309E-08 9.22941E-08 0.00010446  1.4798E-09  1.23838E-06 1.61481E-08 9.70091E-08 1.36846E-09  5.23776E-06 6.52808E-08 1.78921E-05 2.03043E-07 0.009491479 9.80495E-05 1.15833E-06 1.53177E-08 8.61812E-08 1.44309E-09  601-1  4.92527E-06 5.43986E-08 1.61739E-05 1.83596E-07 0.007526811 7.77686E-05 8.52694E-07 1.09198E-08 6.04104E-08  8.7591E-10  601-2  5.10298E-06 6.31619E-08 1.68336E-05 1.90714E-07  8.78955E-05 1.01648E-06 1.31331E-08 7.36128E-08  1.0397E-09  5.08949E-06 5.62884E-08 1.68498E-05 1.91256E-07 0.008206326 8.47778E-05 9.64132E-07 1.24239E-08 7.02452E-08  1.168E-09  534G-1  0.00851417  Air  5.33518E-06 6.61699E-08 1.83193E-05 2.07792E-07 0.009411608 9.72288E-05 1.14207E-06 1.46922E-08 8.64146E-08 1.68523E-09  533G-2  2.57143E-06 3.19129E-08 9.22021E-06 1.04621E-07 0.004814974 4.97383E-05 5.94157E-07 7.64506E-09 4.51459E-08 6.29289E-10  533G-1  5.44776E-06 6.01694E-08 1.88977E-05 2.14341E-07 0.009684527 0.000100089 1.23466E-06 1.58311E-08 9.42306E-08 1.24425E-09  9016G-1  5.15256E-06 5.69208E-08 1.74743E-05 1.98176E-07 0.008597246 8.88256E-05 1.01982E-06 1.32279E-08 6.96785E-08 1.11653E-09  9014G-1  4.82272E-06  5.9841E-08  1.59469E-05 1.81059E-07 0.007390561 7.63555E-05  8.316E-07  1.11172E-08 5.77262E-08 1.49559E-09  174  Vapor  He (cc/cc)  601-5  5.75252E-06 6.74082E-08  0.009417392 9.73078E-05 1.11734E-06  601-5  5.81062E-06 6.80973E-08  0.009399146 9.71083E-05 1.12441E-06 1.48646E-08 8.38284E-08 1.93993E-09  5.6983E-08  Ne (cc/cc)  Ne Err  Ar (cc/cc)  Ar Err  Kr (cc/cc)  Kr Err  Xe (cc/cc)  Xe Err  1.4362E-08  8.54253E-08  1.3631E-09  1.76289E-05 1.99971E-07 0.008866828 9.15894E-05 1.06241E-06 1.38362E-08 8.21735E-08  1.0952E-09  532G-4  4.90805E-06 6.18681E-08 1.85715E-05 2.10755E-07 0.010170676 0.000105081 1.26947E-06 1.63787E-08 9.31091E-08  1.7475E-09  532G-3  5.40502E-06 5.97064E-08 1.89953E-05 2.15462E-07 0.009987539 0.000103176 1.22909E-06 1.56203E-08  1.37192E-09  532G-6  6.33246E-06 6.99638E-08 1.79692E-05 2.03862E-07  532G-5  4.84641E-06 5.35488E-08  9017G-1  5.15699E-06  He Err  1.7774E-05  0.00969899  0.000100185  1.1942E-06  9.4916E-08  1.57675E-08 9.15298E-08 1.71213E-09  2.01672E-07 0.009759036 0.000100858 1.21331E-06 1.55261E-08 9.18226E-08 1.49271E-09  175  Table B.2. Noble gas isotope ratio dataset for vadose zone gas analyzed through noble gas extraction lines and mass spectrometry at EAWAG during 2008 sampling event, Bemidji, Minnesota Vapor Well  3  He/4He  3  He/4He Err  22  Ne/20Ne  22  Ne/20Ne Err  40  Ar/36Ar  40  Ar/36Ar Err  601-5  1.3314E-06 4.35465E-08 0.10211  0.000375  INF  601-7  1.23052E-06 1.1039E-08  0.10197  0.000152  296.234662  0.770913349  601-6  1.28859E-06 2.13758E-08 0.10221  0.000139  296.234662  0.604775808  601-3  1.37751E-06 1.36948E-08 0.10181  0.000177  295.3582281  0.43167741  310G-1  1.42394E-06 1.24439E-08 0.10197  0.0000588  295.3582281 0.176515864  601-4  1.40157E-06 1.77559E-08 0.10235  0.0000973  295.3582281 0.391480728  532G-2  1.38596E-06 1.87135E-08 0.10182  0.000235  294.4869648 0.990310147  601-1  1.38755E-06 1.2008E-08  0.10155  0.000102  293.6208267 0.263395153  601-2  2.92453E-07 2.66038E-07 0.10194  0.000104  294.4869648 0.221516743  534G-1  1.43582E-06 1.51343E-08 0.10197  0.0000765  294.4869648 0.157233453  Air  1.36073E-06 1.67123E-08 0.10213  0.000171  295.3582281 0.812672048  533G-2  1.41951E-06 1.57561E-08 0.10207  0.000149  296.234662  533G-1  1.43108E-06 9.42356E-09 0.10209  0.0000657  294.4869648 0.363113721  9016G-1 1.43035E-06 9.82587E-09 0.10198  0.000103  294.4869648 0.233678447  9014G-1 1.33094E-06 1.92086E-08 0.10183  0.000396  294.4869648 0.348345938  0.273379762  601-5  1.39409E-06 1.4532E-08  294.4869648 0.559438364  601-5  1.40556E-06 1.88333E-08  295.3582281 0.602076388  9017G-1 1.39655E-06 1.30172E-08 0.10201  0.000178  294.4869648 0.721883976  532G-4  1.38764E-06 1.96067E-08 0.10241  0.0000802  296.234662  532G-3  1.41634E-06 1.15953E-08 0.10206  0.00007  295.3582281 0.126706932  532G-6  1.1711E-06 1.35361E-08  0.1024  0.000108  296.234662  0.409630126  532G-5  1.36364E-06 1.61953E-08 0.10252  0.00012  296.234662  0.434243095  0.416662403  176  Appendix C Table C.1. Geological bore hole logs recorded at monitoring well 423, situated south east of well 601 Depth from (m)  Depth to (m)  Geologic Description  0.0  1.5  Sand; fine to medium  1.5  2.1  Sand; fine to medium and medium to course gravel  2.1  7.9  Sand; fine to medium, (oil last .3048m)  177  Appendix D Table D.1. Noble gas dataset for dissolved gas analyzed through noble gas extraction lines and mass spectrometry at EAWAG during 2008 sampling event, Bemidji, Minnesota. 3  He Err He (cc/g)  He Err  Ne (cc/g)  Ne Err  Ar (cc/g)  310E 8.37E-14  2.E-15 4.27E-08  5.E-10  1.89E-07  2.E-09  531A 1.18E-13  2.E-15 8.31E-08  7.E-10  2.85E-07  532A 1.74E-14  6.E-16 1.17E-08  1.E-10  533C 7.09E-14  1.E-15 3.61E-08  533B 6.83E-14 534B 3.03E-14  MW  3  He (cc/g)  Ar Err  Kr (cc/g)  Kr Err  Xe (cc/g)  Xe Err  4.03E-04 4.E-06 9.57E-08  1.E-09 1.45E-08  4.E-10  3.E-09  3.12E-04 3.E-06 6.59E-08  8.E-10 9.20E-09  3.E-10  4.44E-08  4.E-10  1.68E-04 1.E-06 4.69E-08  6.E-10 8.40E-09  2.E-10  3.E-10  1.61E-07  2.E-09  3.87E-04 3.E-06 9.40E-08  1.E-09 1.49E-08  4.E-10  1.E-15 9.91E-08  8.E-10  1.49E-07  1.E-09  3.21E-04 2.E-06 7.85E-08  9.E-10 1.28E-08  3.E-10  8.E-16 2.12E-08  2.E-10  6.92E-08  7.E-10  1.73E-04 1.E-06 4.43E-08  6.E-10 7.56E-09  2.E-10  315 1.65E-14 5.E-16 1.18E-08 1.E-10 3.98E-08 4.E-10 8.24E-05 6.E-07 4.26E-08 3.E-09 6.75E-09 2.E-10 Table D.2. Noble gas isotope ratio dataset for dissolved gas analyzed through noble gas extraction lines and mass spectrometry at EAWAG during 2008 sampling event, Bemidji, Minnesota. 3  He/4He  Err. 3He/4He  22  Ne/20Ne  Err. 22Ne/20Ne  40  Ar/36Ar  Err. 40Ar/36Ar  1.95868E-06  3.79969E-08  0.10246  0.00031462  299.6670501  2.532246842  1.42041E-06  1.60837E-08  0.102  0.00025002  297.0190744  1.466847049  1.48013E-06  4.74766E-08  0.10265  0.0013836  293.7072112  2.863450887  1.96467E-06  3.42753E-08  0.10186  0.00038459  297.5945898  2.034529995  6.8981E-07  9.24193E-09  0.10245  0.00036188  295.9887366  1.117680429  1.42884E-06  3.52954E-08  0.10059  0.00068619  294.1658988  3.072199061  1.40038E-06  4.15151E-08  0.10234  0.0010298  304.1497763  16.07343028  178  Appendix E  TITLE Well 315-no diffusion SOLUTION_MASTER_SPECIES [N2] [N2] 0.0 28.02 14.01 [Ar] [Ar] 0.0 [Ar] 39.95 [He] [He] 0.0 [He] 4.0020602 [Ne] [Ne] 0.0 [Ne] 20.1797 [Kr] [Kr] 0.0 [Kr] 83.8 [Xe] [Xe] 0.0 [Xe] 131.29 [C](-4) [C]H4 0.0 [C]H4 12.011 [C] H[C]O31.0 H[C]O3 12.0110 [C](4) H[C]O31.0 H[C]O3 12.0110 [X] [X] 0.0 [X] 1 SOLUTION_SPECIES [X] = [X] log_k 0.0 delta_h 0.0 kcal [N2] = [N2] log_k 0.0 delta_h 0.0 kcal [Ar] = [Ar] log_k 0.0 delta_h  0.0 kcal  [He] = [He] log_k delta_h  0.0 0.0 kcal  [Ne] = [Ne] log_k delta_h  0.0 0.0 kcal  [Kr] = [Kr] log_k delta_h  0.0 0.0 kcal  [Xe] = [Xe] log_k delta_h  0.0 0.0 kcal  H[C]O3- = H[C]O3log_k 0 -delta_H 0 [C]H4 = [C]H4 log_k 0.0 delta_h 0.0 kcal  1.0000 H[C]O3- + 1.0000 H+ = [C]O2 +1.0000 H2O log_k +6.3447 -delta_H -9.7027 -analytic -1.0534e+001 2.1746e-002 2.5216e+003 7.9125e-001 3.9351e+001 1.0000 H[C]O3- = [C]O3-- +1.0000 H+ log_k -10.3288 -delta_H 14.6984 -analytic -6.9958e+001 -3.3526e-002 7.0846e+001 2.8224e+001 -1.0849e+000 H+ + H[C]O3- + H2O = [C]H4 + 2 O2 log_k -144.1412 delta_h 863.599 kJ/mol  PHASES Xgas [X] = [X] log_k -6 delta_h 0.0 kcal N2gas [N2] = [N2] log_k -3.0696 delta_h 0.0 kcal Argas [Ar] = [Ar] log_k -2.7304 delta_h 0.0 kcal Hegas [He] = [He] log_k -3.3929 delta_h 0.0 kcal Negas [Ne] = [Ne] log_k -3.2956 delta_h 0.0 kcal Krgas [Kr] = [Kr] log_k -2.4414 delta_h 0.0 kcal Xegas [Xe] = [Xe] log_k -2.1625 delta_h 0.0 kcal CH4gas [C]H4 = [C]H4 log_k -2.7227 -delta_H 0.0 kJ/mol CO2gas  179  [C]O2 +1.0000 H2O = + 1.0000 H+ + 1.0000 H[C]O3log_k -7.8136 -delta_H -10.5855 kJ/mol # Calculated enthalpy of reaction CO2(g) -analytic -8.5938e+001 -3.0431e-002 2.0702e+003 3.2427e+001 3.2328e+001 RATES Hegas_diff-1 -start 10 delz = 0.075 20 D_He_eff = 1.608E-9 30 C_He_vad = 2.08E40 flux_diff_He = D_He_eff * (C_He_vad MOL("[He]"))/delz 50 rate = flux_diff_He 60 moles = rate*TIME 70 SAVE moles -end Negas_diff-1 -start 10 delz = 0.075 20 D_Ne_eff = 8.22E-10 30 C_Ne_vad = 8.86E-9 40 flux_diff_Ne = D_Ne_eff * (C_Ne_vad - MOL("[Ne]"))/delz 50 rate = flux_diff_Ne 60 moles = rate*TIME 70 SAVE moles -end Argas_diff-1 -start 10 delz = 0.075 20 D_Ar_eff = 7.5E-10 30 C_Ar_vad = 1.6E-5 40 flux_diff_Ar = D_Ar_eff * (C_Ar_vad MOL("[Ar]"))/delz 50 rate = flux_diff_Ar 60 moles = rate*TIME 70 SAVE moles -end Krgas_diff-1 -start 10 delz = 0.075 20 D_Kr_eff = 3.21E-10 30 C_Kr_vad = 3.69E-9 40 flux_diff_Kr = D_Kr_eff * (C_Kr_vad MOL("[Kr]"))/delz 50 rate = flux_diff_Kr 60 moles = rate*TIME 70 SAVE moles -end Xegas_diff-1 -start 10 delz = 0. water table in [m]  20 D_Xe_eff = 2.49E-10 30 C_Xe_vad = 4.79E-10 40 flux_diff_Xe = D_Xe_eff * (C_Xe_vad MOL("[Xe]"))/delz 50 rate = flux_diff_Xe 60 moles = rate*TIME 70 SAVE moles -end N2gas_diff-1 -start 10 delz = 0.075 20 D_N2_eff = 6.0E-10 30 C_N2_vad = 6.05E40 flux_diff_N2 = D_N2_eff * (C_N2_vad MOL("[N2]"))/delz 50 rate = flux_diff_N2 60 moles = rate*TIME 70 SAVE moles -end Hegas_diff-2 -start 10 delz = 0.225 20 D_He_eff = 1.608E-9 # Helium 30 C_He_vad = 2.08E-9 # dissolved molar He 40 flux_diff_He = D_He_eff * (C_He_vad MOL("[He]"))/delz 50 rate = flux_diff_He 60 moles = rate*TIME 70 SAVE moles -end Negas_diff-2 -start 10 delz = 0.225 20 D_Ne_eff = 8.22E-10 # Neon 30 C_Ne_vad = 8.86E-9 # dissolved molar Ne 40 flux_diff_Ne = D_Ne_eff * (C_Ne_vad MOL("[Ne]"))/delz 50 rate = flux_diff_Ne 60 moles = rate*TIME 70 SAVE moles -end Argas_diff-2 -start 10 delz = 0.225 20 D_Ar_eff = 7.5E-10 # Argon 30 C_Ar_vad = 1.6E-5 # dissolved molar Ar 40 flux_diff_Ar = D_Ar_eff * (C_Ar_vad MOL("[Ar]"))/delz 50 rate = flux_diff_Ar 60 moles = rate*TIME 70 SAVE moles -end Krgas_diff-2 -start 10 delz = 0.225 20 D_Kr_eff = 3.21E-10 # Krypton 30 C_Kr_vad = 3.69E-9 # dissolved molar He  180  40 flux_diff_Kr = D_Kr_eff * (C_Kr_vad MOL("[Kr]"))/delz 50 rate = flux_diff_Kr 60 moles = rate*TIME 70 SAVE moles -end Xegas_diff-2 -start 10 delz = 0.225 20 D_Xe_eff = 2.49E-10 # Xenon 30 C_Xe_vad = 4.79E-10 # dissolved molar Xe 40 flux_diff_Xe = D_Xe_eff * (C_Xe_vad MOL("[Xe]"))/delz 50 rate = flux_diff_Xe 60 moles = rate*TIME 70 SAVE moles -end N2gas_diff-2 -start 10 delz = 0.225 20 D_N2_eff = 6.0E-10 # nitrogen gas 30 C_N2_vad = 6.05E-4 # dissolved molar N2 40 flux_diff_N2 = D_N2_eff * (C_N2_vad MOL("[N2]"))/delz 50 rate = flux_diff_N2 60 moles = rate*TIME 70 SAVE moles -end Hegas_diff-3 -start 10 delz = 0.375 20 D_He_eff = 1.608E-9 # Helium 30 C_He_vad = 2.08E-9 # dissolved molar He 40 flux_diff_He = D_He_eff * (C_He_vad MOL("[He]"))/delz 50 rate = flux_diff_He 60 moles = rate*TIME 70 SAVE moles -end Negas_diff-3 -start 10 delz = 0.375 20 D_Ne_eff = 8.22E-10 # Neon 30 C_Ne_vad = 8.86E-9 # dissolved molar Ne 40 flux_diff_Ne = D_Ne_eff * (C_Ne_vad MOL("[Ne]"))/delz 50 rate = flux_diff_Ne 60 moles = rate*TIME 70 SAVE moles -end Argas_diff-3 -start 10 delz = 0.375 20 D_Ar_eff = 7.5E-10 # Argon 30 C_Ar_vad = 1.6E-5 # dissolved molar Ar  40 flux_diff_Ar = D_Ar_eff * (C_Ar_vad MOL("[Ar]"))/delz 50 rate = flux_diff_Ar 60 moles = rate*TIME 70 SAVE moles -end Krgas_diff-3 -start 10 delz = 0.375 20 D_Kr_eff = 3.21E-10 # Krypton 30 C_Kr_vad = 3.69E-9 # dissolved molar He 40 flux_diff_Kr = D_Kr_eff * (C_Kr_vad MOL("[Kr]"))/delz 50 rate = flux_diff_Kr 60 moles = rate*TIME 70 SAVE moles -end Xegas_diff-3 -start 10 delz = 0.375 20 D_Xe_eff = 2.49E-10 # Xenon 30 C_Xe_vad = 4.79E-10 # dissolved molar Xe 40 flux_diff_Xe = D_Xe_eff * (C_Xe_vad MOL("[Xe]"))/delz 50 rate = flux_diff_Xe 60 moles = rate*TIME 70 SAVE moles -end N2gas_diff-3 -start 10 delz = 0.375 20 D_N2_eff = 6.0E-10 # nitrogen gas 30 C_N2_vad = 6.05E-4 # dissolved molar N2 40 flux_diff_N2 = D_N2_eff * (C_N2_vad MOL("[N2]"))/delz 50 rate = flux_diff_N2 60 moles = rate*TIME 70 SAVE moles -end Hegas_diff-4 -start 10 delz = 0.525 20 D_He_eff = 1.608E-9 # Helium 30 C_He_vad = 2.08E-9 # dissolved molar He 40 flux_diff_He = D_He_eff * (C_He_vad MOL("[He]"))/delz 50 rate = flux_diff_He 60 moles = rate*TIME 70 SAVE moles -end Negas_diff-4 -start 10 delz = 0.525 20 D_Ne_eff = 8.22E-10 # Neon 30 C_Ne_vad = 8.86E-9 # dissolved molar Ne  181  40 flux_diff_Ne = D_Ne_eff * (C_Ne_vad MOL("[Ne]"))/delz 50 rate = flux_diff_Ne 60 moles = rate*TIME 70 SAVE moles -end Argas_diff-4 -start 10 delz = 0.525 20 D_Ar_eff = 7.5E-10 # Argon 30 C_Ar_vad = 1.6E-5 # dissolved molar Ar 40 flux_diff_Ar = D_Ar_eff * (C_Ar_vad MOL("[Ar]"))/delz 50 rate = flux_diff_Ar 60 moles = rate*TIME 70 SAVE moles -end Krgas_diff-4 -start 10 delz = 0.525 20 D_Kr_eff = 3.21E-10 # Krypton 30 C_Kr_vad = 3.69E-9 # dissolved molar He 40 flux_diff_Kr = D_Kr_eff * (C_Kr_vad MOL("[Kr]"))/delz 50 rate = flux_diff_Kr 60 moles = rate*TIME 70 SAVE moles -end Xegas_diff-4 -start 10 delz = 0.525 20 D_Xe_eff = 2.49E-10 # Xenon 30 C_Xe_vad = 4.79E-10 # dissolved molar Xe 40 flux_diff_Xe = D_Xe_eff * (C_Xe_vad MOL("[Xe]"))/delz 50 rate = flux_diff_Xe 60 moles = rate*TIME 70 SAVE moles -end N2gas_diff-4 -start 10 delz = 0.525 20 D_N2_eff = 6.0E-10 # nitrogen gas 30 C_N2_vad = 6.05E-4 # dissolved molar N2 40 flux_diff_N2 = D_N2_eff * (C_N2_vad MOL("[N2]"))/delz 50 rate = flux_diff_N2 60 moles = rate*TIME 70 SAVE moles -end  SOLUTION 1 # The initial equilibriation with air at 0.95. Insert log of vadose zone partial pressures units mol/l pH 7 pe 4 density 1 temp 10 redox pe water 1 #kg Equilibrium_Phases CH4gas -1 CO2gas -0.876 O2(g) -12 N2gas -0.1486071 Argas -2.0655015 Negas -4.756962 Hegas -5.2881928 Krgas -5.9913998 Xegas -7.1567672 SAVE solution 1  SELECTED_OUTPUT -File 315nodiffusion.exl -selected_out true -simulation true -state true -solution true -distance false -time false -step true -ph true -pe true -reaction true -totals [Ar] [N2] O2 [C](4) [C](-4) [He] [Ne] [Kr] [Xe] -molalities [He] [Ne] [Ar] [Kr] [Xe] [N2] [C]H4 H[C]O3- O2 -gas CO2gas CH4gas O2(g) Argas N2gas Hegas Negas Krgas Xegas Xgas -inverse_modeling true END USE solution 1 GAS_PHASE 2 -fixed_pressure -volume 0.1 -pressure 0.9575 -temperature 10 Hegas 3.06725e-6 Negas 1.04376e-5  182  Argas 6.29448e-3 Krgas 8.31555e-7 Xegas 6.18098e-8 N2gas 0.453087 CH4gas 0.348591 CO2gas 0.162180 O2(g) 0 Xgas 0 REACTION 1 H[C]O31 [C]H4 1 0.00128 moles in 1 step SAVE solution 5 END USE solution 5 KINETICS 1 Hegas_diff-1 -formula [He] 1 -tol 1e-008 Negas_diff-1 -formula [Ne] 1 -tol 1e-008 Argas_diff-1 -formula [Ar] 1 -tol 1e-008 Krgas_diff-1 -formula [Kr] 1 -tol 1e-008 Xegas_diff-1 -formula [Xe] 1 -tol 1e-008 N2gas_diff-1 -formula [N2] 1 -tol 1e-008 -steps 2160000 in 1 steps # seconds -step_divide 1 -runge_kutta 3 SAVE solution 6 END USE solution 6 GAS_PHASE 3 -fixed_pressure -volume 0.1 -pressure 0.98 -temperature 10 Hegas 2.20293e-6 Negas 7.49136e-6 Argas 4.76687e-3 Krgas 6.76600e-7 Xegas 5.42122e-8 N2gas 0.327185 CH4gas 0.476967  CO2gas 0.182863 O2(g) 0 Xgas 0 REACTION 2 H[C]O3[C]H4 1  1  0.00128 moles in 1 step SAVE solution 7 END USE solution 7 KINETICS 2 Hegas_diff-2 -formula [He] 1 -tol 1e-008 Negas_diff-2 -formula [Ne] 1 -tol 1e-008 Argas_diff-2 -formula [Ar] 1 -tol 1e-008 Krgas_diff-2 -formula [Kr] 1 -tol 1e-008 Xegas_diff-2 -formula [Xe] 1 -tol 1e-008 N2gas_diff-2 -formula [N2] 1 -tol 1e-008 -steps 2160000 in 1 steps # seconds -step_divide 1 -runge_kutta 3 SAVE solution 8 END USE solution 8 GAS_PHASE 4 -fixed_pressure -volume 0.1 -pressure 1.0175 -temperature 10 Hegas 1.54030e-6 Negas 5.98159e-6 Argas 3.84291e-3 Krgas 5.65468e-7 Xegas 4.78794e-8 N2gas 0.260912 CH4gas 0.561825 CO2gas 0.203174 O2(g) 0 Xgas 0 REACTION 3  183  H[C]O3[C]H4 1  1  0.00128 moles in 1 step SAVE solution 9 END USE solution 9 KINETICS 3 Hegas_diff-3 -formula [He] 1 -tol 1e-008 Negas_diff-3 -formula [Ne] 1 -tol 1e-008 Argas_diff-3 -formula [Ar] 1 -tol 1e-008 Krgas_diff-3 -formula [Kr] 1 -tol 1e-008 Xegas_diff-3 -formula [Xe] 1 -tol 1e-008 N2gas_diff-3 -formula [N2] 1 -tol 1e-008 -steps 2160000 in 1 steps # seconds -step_divide 1 -runge_kutta 3  SAVE solution 11 END USE solution 11 KINETICS 4 Hegas_diff-4 -formula [He] 1 -tol 1e-008 Negas_diff-4 -formula [Ne] 1 -tol 1e-008 Argas_diff-4 -formula [Ar] 1 -tol 1e-008 Krgas_diff-4 -formula [Kr] 1 -tol 1e-008 Xegas_diff-4 -formula [Xe] 1 -tol 1e-008 N2gas_diff-4 -formula [N2] 1 -tol 1e-008 -steps 2160000 in 1 steps # seconds -step_divide 1 -runge_kutta 3 SAVE solution 12 END  SAVE solution 10 END USE solution 10 GAS_PHASE 5 -fixed_pressure -volume 0.1 -pressure 1.07 -temperature 10 Hegas 1.45302e-6 Negas 5.05053e-6 Argas 3.27092e-3 Krgas 4.88875e-7 Xegas 4.29060e-8 N2gas 0.220862 CH4gas 0.635545 CO2gas 0.223334 O2(g) 0 Xgas 0 REACTION 4 H[C]O3[C]H4 1  1  0.00128 moles in 1 step  184  Appendix F  Viability of SF6 as a Tracer for Ebullition in the Presence of Hydrocarbons  The approximate detection limit of SF6 with the OmniStar Gas Analyzer is 0.001%. In one liter of air at standard temperature and pressure, there are approximately 0.042 moles of air. Therefore, approximately 4.2x10-6 moles of SF6 must be present per litre of air. Table F.1 serves as a reference for tracer suitability. The Table assumes that the percent saturation of air in the saturated zone is 10%, which borders the lower limit of required pore space air saturation values prior to ebullition. This concept is investigated further in Part 2 of Chapter 4. Table F.1 details the approximate moles of gas exiting a system. Columns segregate calculations based on the percent of the gas in the pore space of the saturated zone that is exiting a system; rows indicate possible volumes of oil with which the bubble equilibrates. The grey volumes signify readings that are below detection limits so long as the measurement is collected from the point of vadose zone entry; the accuracy in the reading will decrease with distance from the point of entry.  Table F.1. Detection potentials for SF6 as a tracer for ebullition, in a hydrocarbon setting, with a maximum gas saturation rate of 10% % Air Exiting  100  50  10  1  n/a  2.58E-04  1.29E-04  2.58E-05  2.58E-06  1  2.56E-04  1.27E-04  2.40E-05  1.49E-06  50  1.89E-04  7.45E-05  5.54E-06  6.87E-08  100  1.49E-04  5.24E-05  3.10E-06  3.48E-08  1000  3.10E-05  8.26E-06  3.48E-07  3.53E-09  Vol (cc) of Oil  185  The calculations used to obtain the values presented in Table F.1 are detailed below. The table does not take into account diffusion of gas in the vadose zone nor does it consider kinetic effects or distances traveled by the bubble. The calculations assume that gas bubbles form in water saturated with SF6 at 1 atm and 20°C as well as assuming that the SF6 partitions from the bubble into the oil (if oil is present in the system). The saturation of water with SF6 at 1 atm is difficult to achieve in large volumes of water (greater than 2 litres) or water that is saturated with gases. The extent to which ebullition occurs has the largest impact on the usefulness of SF6 as a tracer; partitioning will impede the effectiveness of SF6 as a tracers in the presence of hydrocarbons.  Calculations for Partitioning Experiment 1. KG−1W =  A VA = 149 W VW  where: A = moles of gas in air phase W = moles in water phase VA = volume of air phase VW =volume of water phase 2. A + W = 2.75 ×10−4 - sub 1. into 2. - sub volume of bubble into volume of A1 - solve from moles in bubble A1 = A2 + O = X A1 = moles of SF6 in bubble A2 = moles of SF6 in bubble after encountering oil O = moles in oil -sub volumes of bubble and oil into equation O KO−W = = 0.73 A2 -solve for moles of [A2]  186  Appendix G. Table G.1. Column physical parameters and headspace mole fractions for the column experiment Time w.l. rise Temp. Days  Cm  ± 0.001 ± 0.05  C  w.l. vol. Change cc  ± 0.05  −  Headspace Col. Press Vol cc KPa ±1  0  ±  0.0  983  43.30  42  ±  0.0  940  4.9  43.50  53  ±  0.1  930  6.0  44.10  85  ±  0.1  898  127  ±  0.1  855  138  ±  0.2  845  143  ±  0.2  839  z  42.50  2.3  8.0  20.00  44.90  10.0  45.10  11.0  45.20  20.60  ± 0.01  Pres. Initial Moles Molar Releas. Increase KPa mol mol ± 0.01  ± 0.0001  ± 0.0001  Vol. Released cc  Cumulative Vol. Cc  CH4 %  %  %  %  %  ±1  ±1  ±5  ±5  ±5  ±5  ±5  21  0  0.93  21  0  0.93  11.9  45.40  20.70  154  ±  0.2  829  101.6  0.00  0.0345  0.0345  0  0  12.1  45.40  23.60  154  ±  0.2  829  103.55  0.00  0.0348  0.0348  0  0  O2  CO2  Ar  SF6  0.93  12.1  45.40  23.60  154  ±  0.2  829  100.8  2.75  0.0348  0.0348  22  22  17  17  0.89  14.3  45.50  20.00  159  ±  0.2  824  103.6  0.00  0.0350  0.0359  0  22  18  19  0.98  22  16  0.98  23  13  23  3  1.17 1.17  0.000  14.3  45.40  20.00  154  ±  0.2  829  101.9  1.70  0.0352  0.0362  14  36  15.0  45.40  20.00  154  ±  0.2  829  103.35  0.00  0.0351  0.0367  0  36  15.0  45.40  20.00  154  ±  0.2  829  102.15  1.20  0.0351  0.0367  10  46  17.9  45.40  18.60  154  ±  0.2  829  107.55  0.00  0.0368  0.0387  0  46  154  ±  0.2  829  104  3.35  0.0364  0.0383  27  73  18.0  45.40  20.90  18.9  45.40  20.00  154  ±  0.2  829  101.65  4.90  0.0362  0.0393  40  113  21.0  45.70  20.00  170  ±  0.2  813  104.6  0.00  0.0349  0.0395  0  113  3  1.13  21.0  45.40  20.00  154  ±  0.2  829  102.4  2.20  0.0356  0.0403  18  131  21.2  45.70  19.20  170  ±  0.2  813  100.3  1.20  0.0339  0.0393  10  141  23  3  0.2  813  99  2.10  0.0338  0.0396  17  158  24  0  29  1.21  0.000  0.2 0.2  813 813  104.25 102.45  0.00 1.80  0.0349 0.0349  0.0414 0.0414  0 14  158 172  24  0  32  1.34  0.000 0.021  22.0  45.70  19.20  170  ±  25.0 25.0  45.70 45.70  18.80 18.80  170 170  ± ±  187  Time  wzz.l. rise  Temp .  w.l. vol. Change  Headspa ce Vol  Col. Press  Pres. Releas.  Initial Moles  Molar Increase  Vol. Released  Cumulative Vol.  CH4  O2  CO2  Ar  SF6  Days  Cm  C  cc  cc  KPa  KPa  mol  mol  cc  cc  %  %  %  %  %  ± 0.05  −  ±5  ±5  ±5  ±5  38  1.09  ± 0.001 ± 0.05  ±1  ± 0.01  ± 0.01  ± 0.0001  ± 0.0001  ±1  ±1  ±5  26.0  45.90  19.10  180  ±  0.2  802  104.675  0.00  0.0346  0.0416  0  172  24  26.0  45.00  19.10  133  ±  0.1  850  102.4  2.30  0.0366  0.0440  19  192  0.022  28.0  45.20  19.10  143  ±  0.2  839  102.05  0.63  0.0355  0.0436  5  197  0.095  32.3  45.00  20.30  133  ±  0.1  850  111.5  0.00  0.0389  0.0473  0  197  32.3  45.30  20.30  149  ±  0.2  834  107.5  4.00  0.0381  0.0464  33  230  175  ±  0.2  808  102.35  5.20  0.0356  0.0449  41  271  32.3  45.80  20.30  34.3  46.00  20.30  186  ±  0.2  797  103.45  2.30  0.0345  0.0454  18  289  36.3  46.00  20.30  186  ±  0.2  797  103.45  6.00  0.0358  0.0474  47  336  36.9  46.00  20.30  186  ±  0.2  797  105.85  0.00  0.0346  0.0482  0  336  36.9  46.00  20.30  186  ±  0.2  797  102.65  3.20  0.0346  0.0482  25  361  38.9  46.00  18.00  186  ±  0.2  797  106.3  0.00  0.0350  0.0498  0  361  39.0  46.00  18.00  186  ±  0.2  797  105  1.30  0.0350  0.0498  10  372  40.1  46.00  21.20  186  ±  0.2  797  103.85  3.70  0.0350  0.0500  29  401  42.1  46.00  21.10  186  ±  0.2  797  105.85  3.20  0.0355  0.0518  25  426  186  ±  0.2  797  107.2  0.00  0.0351  0.0525  0  426  43.0  46.00  19.30  43.0  46.00  19.30  186  ±  0.2  797  103.9  3.30  0.0351  0.0525  26  452  44.0  46.00  20.20  186  ±  0.2  797  107  0.00  0.0350  0.0534  0  452  44.0  46.00  20.20  186  ±  0.2  797  104.9  2.10  0.0350  0.0534  17  468  45.1  46.00  19.80  186  ±  0.2  797  102  4.70  0.0349  0.0540  37  505  47.0  46.00  20.40  186  ±  0.2  797  102.55  4.00  0.0348  0.0554  31  537  47.9  46.00  20.40  186  ±  0.2  797  105.125  0.00  0.0343  0.0562  0  537  47.9  46.00  20.40  186  ±  0.2  797  103.525  1.60  0.0343  0.0562  13  549  48.9  46.00  20.30  186  ±  0.2  797  105.125  0.00  0.0343  0.0568  0  549  48.9  46.00  20.30  186  ±  0.2  797  102.775  2.35  0.0343  0.0568  18  568  49.8  46.00  20.30  186  ±  0.2  797  104.55  0.00  0.0342  0.0574  0  568  49.8  46.00  20.30  186  ±  0.2  797  102.225  2.33  0.0342  0.0574  18  586  ±  0.2  797  103.925  0.00  0.0342  0.0584  0  586  0.2  797  101.65  2.28  0.0342  0.0584  18  604  52.1  46.00  18.10  186  52.1  46.00  18.10  186  ±  25  1.04 0.082  0.101 25  31  0.76  0.144 0.144  0.049 0.086 24  32  25  33  24  31  0.76  25  29  0.82  0.111 0.67  0.101 0.102 0.113  25  24  0.71  0.110  188  Time w.l. rise Temp. Days  Cm  ± 0.001 ± 0.05  w.l. vol. Change  C  cc  ± 0.05  −  Headspace Vol Col. Press cc  Pres. Molar Releas. Initial Moles Increase  Vol. Released  Cumulative Vol.  CH4  O2  CO2  Ar  SF6  cc  %  %  %  %  %  ±5  ±5  KPa  KPa  mol  mol  cc  ±1  ± 0.01  ± 0.01  ± 0.0001  ± 0.0001  ±1  ±1  ±5  54.1  46.00  18.10  186  ±  0.2  797  106.75  0.00  0.0351  0.0600  0  604  25  54.1  46.00  18.10  186  ±  0.2  797  104.2  2.55  0.0351  0.0600  20  624  56.1  46.00  17.80  186  ±  0.2  797  105.9  0.00  0.0349  0.0607  0  624  56.1  46.00  17.80  186  ±  0.2  797  103.3  2.60  0.0349  0.0607  21  645  58.1  46.00  20.10  186  ±  0.2  797  107.1  0.00  0.0350  0.0614  0  645  186  ±  0.2  797  105.525  1.58  0.0350  0.0614  12  657  58.1  46.00  20.10  59.8  46.00  21.10  186  ±  0.2  797  105.45  3.13  0.0354  0.0622  24  682  62.1  46.00  23.00  186  ±  0.2  797  106.575  0.00  0.0345  0.0633  0  682  62.1  46.00  23.00  186  ±  0.2  797  102.975  3.60  0.0345  0.0633  28  710  68.2  46.00  0.00  186  ±  0.2  797  102.59  8.00  0.0388  0.0713  68  777  71.1  46.00  0.00  186  ±  0.2  797  102.4  4.08  0.0374  0.0727  34  812  74.9  46.00  0.00  186  ±  0.2  797  102.2  6.25  0.0381  0.0748  53  864  78.1  46.00  0.00  186  ±  0.2  797  102.31  3.40  0.0371  0.0760  29  893  81.8  46.50  0.00  212  ±  0.2  770  102.49  6.75  0.0371  0.0759  55  948  212  ±  0.2  770  104.15  2.30  0.0333  0.0711  17  965  83.1  46.50  23.50  84.3  46.50  20.50  212  ±  0.2  770  104.95  0.00  0.0331  0.0721  0  965  84.3  46.50  20.50  212  ±  0.2  770  102.65  2.30  0.0331  0.0721  17  983  88.0  44.00  21.00  80  ±  0.1  903  106.1  0.00  0.0392  0.0856  0  983  88.0  44.00  22.00  80  ±  0.1  903  102.45  3.65  0.0391  0.0853  32  1015  89.0  44.00  22.00  80  ±  0.1  903  105.025  0.00  0.0387  0.0863  0  1015  89.0  44.00  22.00  80  ±  0.1  903  102.95  2.08  0.0387  0.0863  18  1033  90.9  46.00  20.40  186  ±  0.2  797  105.95  0.00  0.0346  0.0775  0  1033  90.9  46.00  20.40  186  ±  0.2  797  103.25  2.70  0.0346  0.0775  21  1055  94.9  46.00  20.40  186  ±  0.2  797  107.9  0.00  0.0352  0.0790  0  1055  94.9  46.00  20.40  186  ±  0.2  797  105.9  2.00  0.0352  0.0790  16  1070  186  ±  0.2  797  107.3  0.00  0.0350  0.0795  0  1070  0.2  797  105.4  1.90  0.0350  0.0795  15  1085  0.2  797  107.625  0.00  0.0351  0.0802  0  1085  95.9  46.00  20.40  95.9  46.00  20.40  186  ±  96.9  46.00  20.40  186  ±  25  13  25  ±5  ±5  0.75  0.060  0.67  0.090  0.71  0.090  0.69  0.100  24  11  0.19  0.031  25  21  0.30  0.070  0.08  0.030  0.23  0.030  26 24  17  189  Time w.l. rise Temp. Days  Cm  ± 0.001 ± 0.05  w.l. vol. Change  C  cc  ± 0.05  −  Headspace Vol Col. Press cc  Pres. Molar Releas. Initial Moles Increase  Vol. Released  Cumulative Vol.  CH4  O2  CO2  Ar  SF6  cc  %  %  %  %  %  ±5  ±5  ±5  KPa  KPa  mol  mol  cc  ±1  ± 0.01  ± 0.01  ± 0.0001  ± 0.0001  ±1  ±1  ±5  97.9  46.00  20.40  186  ±  0.2  797  104.62  0.00  0.0342  0.0806  0  1118  24  0.027  96.9  46.00  20.40  186  ±  0.2  797  105.825  0.00  0.0346  0.0804  0  1105  96.9  46.00  20.40  186  ±  0.2  797  104.125  1.70  0.0346  0.0804  13  1118  97.9  46.00  20.40  186  ±  0.2  797  104.62  0.00  0.0342  0.0806  0  1118  24  0.027  97.9  46.00  20.40  186  ±  0.2  797  100.28  4.34  0.0342  0.0806  34  1152  105.9  46.00  20.30  186  ±  0.2  797  110.1  0.00  0.0360  0.0838  0  1152  24  0.026  106.9  46.00  20.30  186  ±  0.2  797  104.5  5.60  0.0360  0.0838  44  1196  110.8  46.00  20.50  186  ±  0.2  797  108.48  0.00  0.0354  0.0851  0  1196  110.8  46.00  20.50  186  ±  0.2  797  104.98  3.50  0.0354  0.0851  27  1224  115.8  46.00  20.60  186  ±  0.2  797  109.68  0.00  0.0358  0.0866  0  1224  115.8  46.00  20.60  186  ±  0.2  797  103.98  5.70  0.0358  0.0866  45  1269  118.7  46.00  20.40  186  ±  0.2  797  107.22  0.00  0.0350  0.0877  0  1269  118.7  46.00  20.40  186  ±  0.2  797  103.41  3.81  0.0350  0.0877  30  1298  ±5  0.016  190  Appendix H  Fick’s Law Calculations for Column Diffusion  J flux = D *  dC dx  J flux = diffusive downwards flux (mol m-2 s-1) D * = effective diffusion coefficient = 7.5 x10-10 (m2 s-1) dC = 0.125375 (mol m-3) This is double the maximum actual estimate to account for bubble partitioning dx = 0.3 (m) This volume is an underestimate of the diffusion length J1flux =  9.76 ×10−6 = 2.42 ×10 − 9 0.0053 × 950400  The flux was calculated by determining the amount of gas in bubble that would pass through the column area, in order for the bubble to have moles such that it is in equilibrium with the atmosphere. The number of moles were determined with a PhreeqC simulation. The time allotted for diffusion is 11 days J 2flux = 7.5 ×10−10  0.125375 = 3.42 ×10−10 0.275  There is a large discrepancy between the two calculated flux values, even when the large and invalid assumptions are applied to the flux values. For this reason it is assumed that replenishment of the OMZ with atmospheric gases is minimal.  191  Table H.1. PhreeqC results for column experiment reaction M_[C]H4 m_HCO3-  m_[N]2  m_He  m_Ne  m_Ar  m_Kr  m_Xe  m_[SF6]  pressure  total mol  volume  g_CO2(g)  0  0.00E+00 1.25E-03 0.00E+00  0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00  0  0.00E+00 1.25E-03 4.46E-04  2.05E-09  8.51E-09 1.41E-05 3.19E-09 4.31E-10 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00  3.10E-03 1.25E-03 1.25E-03 1.13E-04  3.86E-10  1.85E-09 6.63E-06 1.99E-09 3.22E-10 6.62E-06 1.07E+00 4.75E-04 1.07E-02 7.79E-06  3.10E-03 1.26E-03 1.25E-03 4.37E-06  1.04E-11  5.91E-11 6.35E-07 3.29E-10 8.41E-11 1.10E-07 1.07E+00 3.99E-03 8.98E-02 8.64E-04  2.50E-03 1.09E-03 1.25E-03 1.78E-07  2.93E-13  1.99E-12 6.38E-08 5.67E-11 2.28E-11 1.93E-09 1.07E+00 3.79E-03 8.52E-02 1.25E-03  2.30E-03 9.81E-04 1.25E-03 7.11E-09  8.13E-15  6.55E-14 6.30E-09 9.62E-12 6.10E-12 3.31E-11 1.07E+00 3.86E-03 8.68E-02 1.53E-03  2.20E-03 9.13E-04 1.26E-03 2.78E-10  2.21E-16  2.12E-15 6.10E-10 1.60E-12 1.60E-12 5.57E-13 1.07E+00 3.95E-03 8.88E-02 1.73E-03  2.10E-03 8.73E-04 1.26E-03 1.09E-11  6.01E-18  6.87E-17 5.92E-11 2.68E-13 4.23E-13 9.40E-15 1.07E+00 3.93E-03 8.84E-02 1.82E-03  1.95E-03 8.50E-04 1.26E-03 4.50E-13  1.72E-19  2.34E-18 6.02E-12 4.66E-14 1.16E-13 1.66E-16 1.07E+00 3.75E-03 8.42E-02 1.79E-03  1.90E-03 8.36E-04 1.26E-03 1.87E-14  4.97E-21  8.03E-20 6.17E-13 8.19E-15 3.19E-14 2.98E-18 1.07E+00 3.71E-03 8.33E-02 1.80E-03  1.90E-03 8.27E-04 1.26E-03 7.72E-16  1.42E-22  2.73E-21 6.27E-14 1.43E-15 8.74E-15 5.28E-20 1.07E+00 3.74E-03 8.41E-02 1.84E-03  1.90E-03 8.22E-04 1.26E-03 3.17E-17  4.05E-24  9.25E-23 6.34E-15 2.48E-16 2.38E-15 9.32E-22 1.07E+00 3.76E-03 8.46E-02 1.86E-03  1.90E-03 8.19E-04 1.26E-03 1.29E-18  1.15E-25  3.12E-24 6.39E-16 4.28E-17 6.48E-16 1.64E-23 1.07E+00 3.78E-03 8.49E-02 1.88E-03  1.90E-03 8.17E-04 1.26E-03 5.28E-20  0.00E+00  1.05E-25 6.43E-17 7.39E-18 1.76E-16 2.87E-25 1.07E+00 3.79E-03 8.51E-02 1.89E-03  1.90E-03 8.16E-04 1.26E-03 2.15E-21  0.00E+00 0.00E+00 6.46E-18 1.27E-18 4.77E-17 0.00E+00 1.07E+00 3.79E-03 8.52E-02 1.89E-03  1.90E-03 8.15E-04 1.26E-03 8.75E-23  0.00E+00 0.00E+00 6.49E-19 2.19E-19 1.29E-17 0.00E+00 1.07E+00 3.79E-03 8.53E-02 1.89E-03  1.90E-03 8.14E-04 1.26E-03 3.56E-24  0.00E+00 0.00E+00 6.52E-20 3.78E-20 3.50E-18 0.00E+00 1.07E+00 3.80E-03 8.54E-02 1.90E-03  1.90E-03 8.14E-04 1.26E-03 1.45E-25  0.00E+00 0.00E+00 6.54E-21 6.51E-21 9.49E-19 0.00E+00 1.07E+00 3.80E-03 8.54E-02 1.90E-03  192  reaction M_[C]H4 m_HCO3-  m_[N]2  m_He  m_Ne  m_Ar  m_Kr  m_Xe  m_[SF6]  pressure  total mol  volume  g_CO2(g)  1.90E-03 8.14E-04 1.26E-03 0.00E+00  0.00E+00 0.00E+00 6.56E-22 1.12E-21 2.57E-19 0.00E+00 1.07E+00 3.80E-03 8.54E-02 1.90E-03  1.90E-03 8.14E-04 1.26E-03 0.00E+00  0.00E+00 0.00E+00 6.59E-23 1.93E-22 6.97E-20 0.00E+00 1.07E+00 3.80E-03 8.54E-02 1.90E-03  1.90E-03 8.14E-04 1.25E-03 0.00E+00  0.00E+00 0.00E+00 6.61E-24 3.32E-23 1.89E-20 0.00E+00 1.07E+00 3.80E-03 8.54E-02 1.90E-03  1.90E-03 8.14E-04 1.25E-03 0.00E+00  0.00E+00 0.00E+00 6.63E-25 5.72E-24 5.11E-21 0.00E+00 1.07E+00 3.80E-03 8.54E-02 1.90E-03  193  Appendix I  Headspace Mole Fraction Calculations  Headspace concentrations in the system are expressed in terms of volumes. This is done so that the pressure and temperature fluctuations can be normalized to initial conditions. The conditions to which all measurements are normalized are presented in Table 4.8. The calculations presented below convert the mole fraction headspace values into normalized gas volumes. Once normalized gas volumes are established, the moles of gas entering the column can be calculated. The calculations are set up for a simple situation in which the total gas volumes exiting the system are much lower than the total headspace volume; and for systems for which the total amount of gas release is significant.  Provided, the total volume change with time of the system is much less than the total volume of the headspace, the amount of gas entering the headspace as a result of ebullition can be calculated by measuring the accumulated volume of headspace in the column at time t. VT ,i = V( head ),i + ∑ VR V( head ),i  = volume at time i  VT ,i  = total volume of headspace at time i  The initial mole fraction is converted to a volume through the approximation: V( o ), j ≈ VT , j X ( o ), j V( o ), j  = initial volume  X ( o ), j = initial molection of species j 194  The gas removed from the system is considered negligible. As gas is added to the headspace, the mole fraction of that initial headspace gas ( X j.o ) will change, even though the volume of that gas remains the same. X ( o ),i , j =  V( o ), j VT , j  The mole fraction ( X j.ms ) is determined through ion count measurements with the “MS”. The difference between X j.ms and X j.o is equated to the amount of that particular gas entering the headspace by way of ebullition. The total number of moles produced from the biogenic reactions within the column are calculated by the ideal gas law, the approximation holds so long as the initial columns pressure is equal to the final column pressure reading, and the temperature of the system is known and does not fluctuate. Temperature measurements are expected to rise, as temperature generally increases with biological activity. Condensation in the columns suggests temperature changes have occurred within the column. An increase in temperature will increase the calculated volumes as well as the calculated moles of gas produced.  The amount of gas component j entering the headspace is estimated by multiplying X j,ms−0 , by the total number of moles in the headspace. The above approximation is not valid if biogenic gas production is high, and large quantities of gas are being released from the system in comparison to the total volume of the system. In the column experiment, the volume of gas released exceeds that of the initial headspace volume and thus this approximation will not hold and the following calculations are carried out.  The volume of each component gas j released from the system is calculated and subtracted from initial conditions. The volume of initial head space gas ( V j,o ), change in the initial gas volume ( Vo, j,i ) and produced gas ( V j , ms − o ,i ) must be distinguished. The released volume of gas j is calculated by multiplying the measured mole fraction ( X j,ms ) 195  in the system by the volume of gas released at time i. The total contribution of biogenic column gas j ( V j ,CG )to the total volume of gas j is determined by V j , ms ,i = X j , ms ,iVT , ( o ) V j ,CG ,i = V j , ms ,i − Vo , j ,i The amount of gas in the headspace as result of initial conditions is Vo , j ,i = Vo , j ,i −1 − Vo − eb , j ,i Where Veb, j is ebullition gas. The amount of total released gas ( Vr,i, j ) is calculated as describe above. Vr,i is multiplied by either the percentage of gas that enters the headspace from the column or the remaining percentage of gas j that is left over from the initial head space. Vo − eb , j ,i =  VCG − eb , j ,i =  Vo , j ,i Vms , j ,i V j ,CG ,i Vms , j ,i  X j , ms.iVR ,i  X j , ms.iVR ,i  The total amount of column gas can be defined by VT ,CG , j ,i = VCG , j ,i + ∑VCG − eb The total moles of gas entering the headspace from the column is determined by subbing the volume of that gas produced, at initial temperatures and pressures, into the ideal gas law. The above method requires that the mole fraction of each volume release event be known. Unfortunately, this was not possible and a weighted average is used to approximate unknown mole fractions throughout the calculations.  196  Table I.1. Methane headspace volume and mole calculations for column experiment CH4 % 17 18  ±5% ±5%  22  ±5%  23  ±5%  23  ±5%  23 24 24  ±5% ±5% ±5%  24  ±5%  25  ±5%  25  ±5%  Weight. Avg. %  Vol of CH4 cc  Vol. Released cc  Cumul. Vol. cc  Moles Mol  17 18 19 22 22 23 23 23 23 23 23 24 24 24 24 24 24 25 25 25 24 24 24 24 25 25 25 24  143 152 165 184 184 202 200 204 196 200 191 196 201 201 199 211 208 233 228 213 199 209 202 202 207 207 206 207  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  7 8 8 9 9 10 10 10 10 10 10 10 10 10 10 11 11 12 12 11 10 11 10 10 11 11 11 11  3.8 0.0 2.7 0.0 2.1 0.0 6.2 9.4 0.0 4.2 2.3 4.1 0.0 3.5 0.0 4.6 1.3 0.0 8.2 10.3 4.3 11.5 0.0 6.1 0.0 2.5 7.1 6.1  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  0.2 0.0 0.1 0.0 0.1 0.0 0.3 0.5 0.0 0.2 0.1 0.2 0.0 0.2 0.0 0.2 0.1 0.0 0.4 0.5 0.2 0.6 0.0 0.3 0.0 0.1 0.4 0.3  147 156 171 190 192 211 215 228 221 229 222 231 236 239 237 254 252 277 281 276 266 288 281 287 292 295 301 307  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  7 8 8 9 9 10 10 10 10 10 10 10 10 10 10 11 11 12 12 11 10 11 10 10 11 11 11 11  0.0061 0.0065 0.0071 0.0079 0.0080 0.0088 0.0089 0.0095 0.0092 0.0095 0.0092 0.0096 0.0098 0.0100 0.0099 0.0106 0.0105 0.0115 0.0117 0.0115 0.0111 0.0120 0.0117 0.0119 0.0121 0.0123 0.0125 0.0128  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  0.0003 0.0003 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004  24  203  ±  10  0.0  ±  0.0  304  ±  10  0.0126  ±  0.0004  197  CH4 % 24  ±5%  25  ±5%  24  ±5%  25  ±5%  25  ±5%  25  ±5%  25  ±5%  25  ±5%  24  ±5%  Weight. Avg. % 24 24 24 24 25 25 24 24 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 24 24 24  Vol of CH4 cc 203 ± 10 201 ± 10 201 ± 10 203 ± 10 208 ± 11 205 ± 10 198 ± 10 198 ± 10 204 ± 10 203 ± 10 207 ± 11 207 ± 11 206 ± 10 211 ± 11 211 ± 11 209 ± 11 209 ± 11 210 ± 11 210 ± 11 212 ± 11 209 ± 11 209 ± 11 233 ± 12 223 ± 11 225 ± 11 219 ± 11 218 ± 11 193 ± 10 192 ± 10  Vol. Released cc 6.3 ± 0.3 0.0 ± 0.0 3.9 ± 0.2 8.9 ± 0.5 7.8 ± 0.4 0.0 ± 0.0 3.0 ± 0.2 0.0 ± 0.0 4.6 ± 0.2 0.0 ± 0.0 4.6 ± 0.2 0.0 ± 0.0 4.5 ± 0.2 0.0 ± 0.0 5.0 ± 0.3 0.0 ± 0.0 5.1 ± 0.3 0.0 ± 0.0 3.1 ± 0.2 6.1 ± 0.3 0.0 ± 0.0 7.1 ± 0.4 16.9 ± 0.9 8.5 ± 0.4 13.0 ± 0.7 7.0 ± 0.4 13.5 ± 0.7 4.2 ± 0.2 0.0 ± 0.0  Cumul. Vol. cc 310 ± 308 ± 312 ± 322 ± 335 ± 332 ± 328 ± 328 ± 339 ± 338 ± 347 ± 347 ± 350 ± 355 ± 360 ± 358 ± 363 ± 364 ± 367 ± 376 ± 373 ± 380 ± 421 ± 419 ± 434 ± 434 ± 447 ± 427 ± 426 ±  10 10 10 10 11 11 10 10 11 10 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 11 11 10 10  0.0129 0.0128 0.0130 0.0134 0.0139 0.0138 0.0137 0.0137 0.0141 0.0141 0.0144 0.0144 0.0145 0.0147 0.0150 0.0149 0.0151 0.0151 0.0153 0.0156 0.0155 0.0158 0.0175 0.0174 0.0180 0.0181 0.0186 0.0178 0.0177  Moles Mol ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0005 0.0004 0.0004 0.0005 0.0005 0.0005 0.0005 0.0005 0.0004 0.0004  198  CH4 % 25  ±5%  26  ±5%  24  ±5%  24  ±5%  24 24  ±5% ±5%  Weight. Avg. % 24 25 25 26 26 24 24 24 24 24 24 24 24 24 24 24 24 24 24  Vol of CH4 cc 192 ± 10 233 ± 12 232 ± 12 237 ± 12 237 ± 12 203 ± 10 203 ± 10 207 ± 11 207 ± 11 206 ± 10 206 ± 10 206 ± 11 206 ± 11 203 ± 10 203 ± 10 201 ± 10 201 ± 10 211 ± 11 211 ± 11  Vol. Released cc 4.2 ± 0.0 ± 8.0 ± 0.0 ± 4.7 ± 0.0 ± 5.2 ± 0.0 ± 3.8 ± 0.0 ± 3.6 ± 0.0 ± 4.8 ± 0.0 ± 3.3 ± 0.0 ± 8.3 ± 0.0 ± 10.7 ±  0.2 0.0 0.4 0.0 0.2 0.0 0.3 0.0 0.2 0.0 0.2 0.0 0.2 0.0 0.2 0.0 0.4 0.0 0.5  Cumul. Vol. cc 430 ± 470 ± 477 ± 483 ± 488 ± 454 ± 459 ± 463 ± 466 ± 465 ± 469 ± 469 ± 474 ± 470 ± 474 ± 472 ± 480 ± 491 ± 501 ±  10 12 12 12 12 11 11 11 11 11 11 11 11 11 11 10 11 11 11  0.0179 0.0196 0.0199 0.0201 0.0203 0.0189 0.0191 0.0192 0.0194 0.0193 0.0195 0.0195 0.0197 0.0196 0.0197 0.0196 0.0200 0.0204 0.0208  Moles Mol ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  0.0004 0.0005 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005  199  Table I.2. Oxygen headspace volume and mole calculations for column experiment 0 % 17 19  ± 5% ± 5%  16  ± 5%  13  ± 5%  3  ± 5%  3 0 0  ± 5% ± 5% ± 5%  0  ± 5%  Weight. Avg.  Theor. O2  % 17 19 17 16 16 13 13 3 3 3 3 0 0 0 0  cc 173 169 169 167 167 165 165 162 160 160 160 159 159 159 159  Tot. Vol O2 cc 146 158 143 138 138 117 116 30 29 30 28 3.9 4.0 4.0 5.0  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  7 8 7 7 7 6 6 2 1 2 1 0.2 0.2 0.2 1.2  Apprx Vol.  Apprx. O2  Apprx Mol.  cc 3.9 0.0 2.3 0.0 1.6 0.0 3.6 1.4 0.0 0.6 0.3 0.1 0.0 0.1 0.0  cc 27 11 27 29 29 48 49 132 131 131 131 156 155 155 159  mol 0.00720 0.00720 0.00704 0.00704 0.00695 0.00695 0.00688 0.00688 0.00673 0.00667 0.00667 0.00664 0.00663 0.00663 0.00663  200  Table I.3. Argon headspace volume and mole calculations for column experiment Ar  Weight. Avg.  Theor. Ar  %  cc  % 0.93 0.93 0.89 0.98  ± 5% ± 5% ± 5% ± 5%  0.98  ± 5%  1.13  ± 5%  1.17  ± 5%  1.17 1.21 1.34  ± 5% ± 5% ± 5%  1.09  ± 5%  1.04  ± 5%  0.76  ± 5%  0.93 0.89 0.89 0.98 0.98 0.98 0.98 1.13 1.13 1.17 1.17 1.17 1.17 1.17 1.13 1.13 1.09 1.09 1.07 1.04 1.04 1.04 1.00 0.88 0.88 0.88 0.76 0.76 0.75  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  0.09 0.09 0.09 0.10 0.10 0.10 0.10 0.11 0.11 0.12 0.12 0.12 0.12 0.12 0.11 0.11 0.11 0.11 0.11 0.10 0.10 0.10 0.10 0.09 0.09 0.09 0.08 0.08 0.07  8 8 8 8 8 7 7 7 7 7 7 7 7 7 6 6 6 6 6 6 6 6 6 5 5 5 5 5 5  Tot. Vol. Ar cc 7.7 7.5 7.5 8.3 8.3 8.3 8.3 10.0 9.9 10.2 9.8 10.0 9.5 9.5 9.5 9.5 9.1 9.6 9.1 9.7 9.5 8.9 8.3 7.6 7.3 7.3 6.4 6.4 6.3  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.4 0.4 0.4 0.4 0.3 0.3 0.3  Excess Ar  Apprx. Vol. Ar Released  cc  cc  Apprx. Theor. Release cc  0.0 -0.3 -0.3 0.7 0.8 0.9 0.9 2.7 2.6 3.1 3.0 3.2 2.9 3.0 3.1 3.1 2.8 3.3 3.0 3.6 3.4 3.0 2.7 2.1 2.1 2.1 1.3 1.3 1.3  0.00 0.00 0.20 0.00 0.14 0.00 0.10 0.00 0.31 0.47 0.00 0.21 0.11 0.20 0.00 0.16 0.00 0.21 0.06 0.00 0.34 0.43 0.18 0.41 0.00 0.22 0.00 0.08 0.22  0.00 0.00 0.21 0.00 0.12 0.00 0.09 0.00 0.23 0.33 0.00 0.14 0.08 0.14 0.00 0.11 0.00 0.14 0.04 0.00 0.22 0.29 0.12 0.30 0.00 0.16 0.00 0.06 0.17  Apprx. Tot. Excess  Apprx. Excess Moles  cc  mol  0.0 -0.3 -0.3 0.7 0.8 0.9 0.9 2.7 2.7 3.3 3.3 3.5 3.3 3.4 3.5 3.5 3.2 3.8 3.5 4.1 4.1 3.8 3.6 3.0 3.1 3.2 2.4 2.4 2.4  0.00E+00 -1.13E-05 -1.16E-05 3.00E-05 3.21E-05 3.75E-05 3.80E-05 1.12E-04 1.12E-04 1.38E-04 1.36E-04 1.47E-04 1.35E-04 1.40E-04 1.45E-04 1.47E-04 1.34E-04 1.60E-04 1.46E-04 1.72E-04 1.70E-04 1.59E-04 1.48E-04 1.26E-04 1.29E-04 1.31E-04 9.92E-05 9.98E-05 1.01E-04  201  Ar  Weight. Avg.  Theor. Ar  Tot. Vol. Ar  Excess Ar  Apprx. Vol. Ar Released  Apprx. Theor. Release  Apprx. Tot. Excess  Apprx. Excess Moles  %  %  cc  cc  cc  cc  cc  cc  mol  1.4 1.4 1.4 1.5 1.5 1.3 1.5 1.5 1.5 2.2 2.8 2.8 1.9 2.0 2.2 2.6 2.6 2.0 2.0 2.4 2.4 2.5 2.3 2.3 2.1 1.4 0.6 0.4 0.2 -0.8  0.18 0.00 0.19 0.00 0.12 0.25 0.22 0.00 0.08 0.00 0.15 0.00 0.13 0.00 0.13 0.00 0.15 0.00 0.14 0.00 0.09 0.17 0.00 0.19 0.39 0.17 0.20 0.10 0.18 0.04  0.14 0.00 0.14 0.00 0.09 0.20 0.16 0.00 0.06 0.00 0.09 0.00 0.09 0.00 0.08 0.00 0.09 0.00 0.09 0.00 0.05 0.10 0.00 0.12 0.24 0.12 0.17 0.09 0.17 0.05  2.5 2.5 2.6 2.7 2.7 2.6 2.9 2.9 2.8 3.6 4.2 4.2 3.4 3.4 3.7 4.1 4.2 3.6 3.6 4.0 4.1 4.2 4.1 4.1 4.1 3.4 2.6 2.5 2.3 1.3  1.05E-04 1.05E-04 1.06E-04 1.11E-04 1.12E-04 1.09E-04 1.19E-04 1.19E-04 1.17E-04 1.50E-04 1.74E-04 1.77E-04 1.39E-04 1.43E-04 1.56E-04 1.71E-04 1.74E-04 1.48E-04 1.50E-04 1.68E-04 1.69E-04 1.76E-04 1.69E-04 1.72E-04 1.70E-04 1.42E-04 1.09E-04 1.03E-04 9.66E-05 5.30E-05  0.67 0.76  ± 5% ± 5%  0.82  ± 5%  0.71  ± 5%  0.75  ± 5%  0.67  ± 5%  0.71  ± 5%  0.69  ± 5%  0.72 0.71 0.71 0.71 0.71 0.69 0.69 0.68 0.67 0.76 0.82 0.82 0.71 0.71 0.74 0.75 0.75 0.67 0.67 0.71 0.71 0.71 0.69 0.69 0.58 0.50 0.39 0.36 0.33 0.22  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.08 0.08 0.08 0.07 0.07 0.07 0.08 0.08 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.06 0.05 0.04 0.04 0.03 0.02  5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3  6.2 6.0 6.0 6.0 6.0 5.8 5.8 5.6 5.5 6.3 6.8 6.8 5.8 5.8 6.1 6.4 6.4 5.6 5.6 6.0 6.0 6.0 5.8 5.8 5.4 4.5 3.5 3.2 2.9 1.7  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.1 0.1  202  Ar  Weight. Avg.  Theor. Ar  %  cc  % 0.19  ± 5%  0.30  ± 5%  0.08  ± 5%  0.23 0.23  ± 5% ± 5%  0.19 0.19 0.30 0.30 0.08 0.08 0.23 0.23  ± ± ± ± ± ± ± ±  0.02 0.02 0.03 0.03 0.01 0.01 0.02 0.02  2 2 2 2 2 2 2 2  Tot. Vol. Ar  cc 1.5 1.5 2.8 2.8 0.8 0.8 1.9 1.9  ± ± ± ± ± ± ± ±  0.1 0.1 0.1 0.1 0.0 0.0 0.1 0.1  Excess Ar  Apprx. Vol. Ar Released  Apprx. Theor. Release  Apprx. Tot. Excess  Apprx. Excess Moles  cc  cc  cc  cc  mol  -1.0 -1.0 0.4 0.4 -1.6 -1.6 -0.4 -0.4  0.00 0.03 0.00 0.10 0.00 0.02 0.00 0.05  0.00 0.05 0.00 0.08 0.00 0.05 0.00 0.06  1.1 1.1 2.4 2.4 0.5 0.5 1.7 1.6  4.57E-05 4.48E-05 1.02E-04 1.02E-04 2.05E-05 1.92E-05 6.88E-05 6.84E-05  203  Table I.4. SF6 headspace volume and mole calculations for column experiment SF6 % 0.021  ± 5%  0.022 0.095  ± 5% ± 5%  0.082  ± 5%  0.10 0.14 0.14  ± 5% ± 5% ± 5%  0.05 0.09  ± 5% ± 5%  0.11  ± 5%  0.10  ± 5%  0.10  ± 5%  0.11 0.11  ± 5% ± 5%  0.060  ± 5%  Weight. A% 0.021 0.020 0.022 0.095 0.095 0.096 0.082 0.097 0.098 0.098 0.10 0.14 0.14 0.14 0.13 0.12 0.12 0.12 0.12 0.12 0.11 0.11 0.10 0.10 0.10 0.10 0.11 0.11 0.077 0.060 0.060  Tot. Vol. cc 0.17 0.17 0.19 0.81 0.88 0.88 0.71 0.81 0.84 0.81 0.84 1.21 1.21 1.17 1.11 1.05 1.05 1.01 1.01 0.97 0.89 0.88 0.84 0.84 0.84 0.84 0.93 0.90 0.63 0.51 0.51  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  Vol. Released cc 0.01 0.01 0.01 0.04 0.05 0.04 0.04 0.04 0.04 0.04 0.04 0.06 0.06 0.06 0.06 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.03 0.03 0.03  0.004 0.009 0.000 0.024 0.000 0.010 0.024 0.024 0.000 0.025 0.000 0.024 0.053 0.044 0.000 0.016 0.000 0.022 0.000 0.021 0.000 0.019 0.000 0.020 0.000 0.021 0.000 0.014 0.019 0.000 0.017  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  Tot. Vol. cc 0.000 0.000 0.000 0.001 0.000 0.001 0.001 0.001 0.000 0.001 0.000 0.001 0.003 0.002 0.000 0.001 0.000 0.001 0.000 0.001 0.000 0.001 0.000 0.001 0.000 0.001 0.000 0.001 0.001 0.000 0.001  0.18 0.18 0.20 0.84 0.92 0.93 0.78 0.90 0.94 0.94 0.96 1.35 1.35 1.37 1.35 1.30 1.31 1.27 1.29 1.25 1.19 1.18 1.16 1.16 1.18 1.18 1.29 1.27 1.00 0.90 0.90  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  Tot. Moles mol 0.01 0.01 0.01 0.04 0.05 0.04 0.04 0.04 0.04 0.04 0.04 0.06 0.06 0.06 0.06 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.03 0.03 0.03  7.3E-06 7.5E-06 8.5E-06 3.5E-05 3.8E-05 3.9E-05 3.2E-05 3.8E-05 3.9E-05 3.9E-05 4.0E-05 5.6E-05 5.6E-05 5.7E-05 5.6E-05 5.4E-05 5.5E-05 5.3E-05 5.4E-05 5.2E-05 4.9E-05 4.9E-05 4.8E-05 4.8E-05 4.9E-05 4.9E-05 5.4E-05 5.3E-05 4.2E-05 3.7E-05 3.7E-05  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  4.E-07 4.E-07 4.E-07 2.E-06 2.E-06 2.E-06 1.E-06 2.E-06 2.E-06 2.E-06 2.E-06 3.E-06 3.E-06 2.E-06 2.E-06 2.E-06 2.E-06 2.E-06 2.E-06 2.E-06 2.E-06 2.E-06 2.E-06 2.E-06 2.E-06 2.E-06 2.E-06 2.E-06 1.E-06 1.E-06 1.E-06  204  SF6 % 0.090  ± 5%  0.090  ± 5%  0.10  ± 5%  0.031  ± 5%  0.070 0.030  ± 5% ± 5%  0.027  ± 5%  0.026  ± 5%  Weight. A% 0.090 0.090 0.090 0.090 0.092 0.10 0.10 0.085 0.073 0.058 0.054 0.050 0.035 0.031 0.031 0.070 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.027 0.026 0.026 0.026 0.026 0.026  Tot. Vol. cc 0.76 0.76 0.76 0.76 0.78 0.83 0.83 0.79 0.66 0.53 0.48 0.45 0.28 0.25 0.25 0.66 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.22 0.21 0.22 0.22 0.22 0.22  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  Vol. Released cc 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.03 0.03 0.02 0.02 0.01 0.01 0.01 0.03 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01  0.061 0.031 0.047 0.026 0.051 0.017 0.000 0.015 0.000 0.019 0.000 0.009 0.000 0.007 0.000 0.011 0.006 0.000 0.004 0.000 0.010 0.000 0.013 0.000 0.008 0.000 0.012 0.000 0.008 0.000 0.000 0.000  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  Tot. Vol. cc 0.003 0.002 0.002 0.001 0.003 0.001 0.000 0.001 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.001 0.000 0.001 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000  1.16 1.23 1.26 1.31 1.36 1.45 1.47 1.43 1.31 1.19 1.16 1.12 0.96 0.93 0.94 1.35 0.96 0.96 0.97 0.97 0.97 0.98 0.98 0.99 0.99 1.00 0.97 0.97 0.99 0.99 0.99 0.99  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  Tot. Moles mol 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.03 0.03 0.03 0.02 0.02 0.01 0.01 0.03 0.01 0.01 0.02 0.02 0.01 0.01 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01  4.8E-05 5.1E-05 5.2E-05 5.4E-05 5.6E-05 6.0E-05 6.1E-05 6.0E-05 5.5E-05 4.9E-05 4.8E-05 4.7E-05 4.0E-05 3.9E-05 3.9E-05 5.6E-05 4.0E-05 4.0E-05 4.0E-05 4.0E-05 4.0E-05 4.1E-05 4.1E-05 4.1E-05 4.1E-05 4.2E-05 4.0E-05 4.1E-05 4.1E-05 4.1E-05 4.1E-05 4.1E-05  ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±  2.E-06 2.E-06 2.E-06 2.E-06 2.E-06 2.E-06 2.E-06 2.E-06 1.E-06 1.E-06 1.E-06 1.E-06 7.E-07 6.E-07 6.E-07 1.E-06 6.E-07 6.E-07 6.E-07 6.E-07 6.E-07 6.E-07 6.E-07 6.E-07 6.E-07 6.E-07 6.E-07 6.E-07 6.E-07 6.E-07 6.E-07 6.E-07  205  SF6 % 0.016  ± 5%  Weight. A% 0.026 0.016  Tot. Vol. cc 0.22 0.14  ± ±  Vol. Released cc 0.01 0.01  0.000 0.000  ± ±  Tot. Vol. cc 0.000 0.000  0.99 0.91  ± ±  Tot. Moles mol 0.01 0.01  4.1E-05 3.8E-05  ± ±  6.E-07 4.E-07  206  

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